Details

analyze1.7s (9.2%)

Algorithm

1×	search
2×	egg-herbie

Rules

750×	`div-sub_binary64_7926`
723×	`neg-mul-1_binary64_7917`
548×	`neg-sub0_binary64_7916`
545×	`associate-/l*_binary64_7866`
477×	`distribute-frac-neg_binary64_7884`
315×	`associate-/r*_binary64_7865`
295×	`distribute-rgt-in_binary64_7871`
292×	`sub-neg_binary64_7914`
199×	`cancel-sign-sub-inv_binary64_7887`
166×	`distribute-lft-in_binary64_7870`
149×	`*-commutative_binary64_7852`
144×	`associate-/r/_binary64_7867`
141×	`distribute-lft-neg-out_binary64_7880`
136×	`distribute-rgt-neg-out_binary64_7881`
90×	`associate-r_binary64_7861`
83×	`unsub-neg_binary64_7915`
73×	`mul0-rgt_binary64_7904` `mul0-lft_binary64_7903` `associate--r+_binary64_7857`
63×	`div0_binary64_7902` `associate--l-_binary64_7859`
58×	`distribute-rgt-neg-in_binary64_7879` `associate-l_binary64_7862`
37×	`sub0-neg_binary64_7908`
35×	`associate-+l-_binary64_7856` `+-commutative_binary64_7851`
33×	`distribute-neg-in_binary64_7882`
30×	`*-lft-identity_binary64_7910`
27×	`associate-+l+_binary64_7854`
26×	`distribute-lft-neg-in_binary64_7878`
24×	`remove-double-neg_binary64_7909`
23×	`+-lft-identity_binary64_7905`
18×	`associate-/l/_binary64_7868` `associate--r-_binary64_7860`
12×	`--rgt-identity_binary64_7907`
9×	`/-rgt-identity_binary64_7912` `associate--l+_binary64_7858` `associate-+r-_binary64_7855` `associate-+r+_binary64_7853`
7×	`*-rgt-identity_binary64_7911`
5×	`+-rgt-identity_binary64_7906` `swap-sqr_binary64_7888`
1×	`1-exp_binary64_7965` `swap-x-y` `swap-t-a`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_8184` `erf-erfc_binary64_8183` `erf-odd_binary64_8182` `if-if-and-not_binary64_8181` `if-if-and_binary64_8180` `if-if-or-not_binary64_8179` `if-if-or_binary64_8178` `if-not_binary64_8177` `if-same_binary64_8176` `if-false_binary64_8175` `if-true_binary64_8174` `not-gte_binary64_8173` `not-lte_binary64_8172` `not-gt_binary64_8171` `not-lt_binary64_8170` `gte-same_binary64_8169` `lte-same_binary64_8168` `gt-same_binary64_8167` `lt-same_binary64_8166` `sinh---cosh_binary64_8113` `sinh-+-cosh_binary64_8112` `sinh-cosh_binary64_8111` `tanh-def-c_binary64_8110` `tanh-def-b_binary64_8109` `tanh-def-a_binary64_8108` `cosh-def_binary64_8107` `sinh-def_binary64_8106` `tan-neg_binary64_8053` `cos-neg_binary64_8052` `sin-neg_binary64_8051` `tan-0_binary64_8050` `cos-0_binary64_8049` `sin-0_binary64_8048` `hang-m-tan_binary64_8047` `hang-p-tan_binary64_8046` `hang-m0-tan_binary64_8045` `hang-p0-tan_binary64_8044` `hang-0m-tan_binary64_8043` `hang-0p-tan_binary64_8042` `tan-+PI/2_binary64_8041` `tan-+PI_binary64_8040` `tan-PI_binary64_8039` `tan-PI/3_binary64_8038` `tan-PI/4_binary64_8037` `tan-PI/6_binary64_8036` `cos-+PI/2_binary64_8035` `cos-+PI_binary64_8034` `cos-PI_binary64_8033` `cos-PI/2_binary64_8032` `cos-PI/3_binary64_8031` `cos-PI/4_binary64_8030` `cos-PI/6_binary64_8029` `sin-+PI/2_binary64_8028` `sin-+PI_binary64_8027` `sin-PI_binary64_8026` `sin-PI/2_binary64_8025` `sin-PI/3_binary64_8024` `sin-PI/4_binary64_8023` `sin-PI/6_binary64_8022` `sub-1-sin_binary64_8021` `sub-1-cos_binary64_8020` `-1-add-sin_binary64_8019` `-1-add-cos_binary64_8018` `1-sub-sin_binary64_8017` `1-sub-cos_binary64_8016` `cos-sin-sum_binary64_8015` `log-E_binary64_8011` `log-pow_binary64_8010` `log-rec_binary64_8009` `log-div_binary64_8008` `log-prod_binary64_8007` `pow-base-0_binary64_8005` `unpow1/3_binary64_7988` `unpow3_binary64_7987` `unpow2_binary64_7986` `unpow1/2_binary64_7985` `pow-plus_binary64_7984` `exp-to-pow_binary64_7983` `pow-base-1_binary64_7981` `unpow0_binary64_7980` `unpow1_binary64_7979` `unpow-1_binary64_7978` `exp-lft-cube_binary64_7977` `exp-lft-sqr_binary64_7976` `exp-cbrt_binary64_7975` `exp-sqrt_binary64_7974` `exp-prod_binary64_7973` `div-exp_binary64_7972` `rec-exp_binary64_7971` `prod-exp_binary64_7970` `exp-diff_binary64_7969` `exp-neg_binary64_7968` `exp-sum_binary64_7967` `e-exp-1_binary64_7966` `exp-1-e_binary64_7964` `exp-0_binary64_7963` `rem-log-exp_binary64_7962` `rem-exp-log_binary64_7961` `cube-unmult_binary64_7958` `cube-mult_binary64_7951` `cube-div_binary64_7950` `cube-prod_binary64_7949` `cube-neg_binary64_7948` `rem-3cbrt-rft_binary64_7947` `rem-3cbrt-lft_binary64_7946` `rem-cbrt-cube_binary64_7945` `rem-cube-cbrt_binary64_7944` `sqr-abs_binary64_7936` `sqr-neg_binary64_7935` `rem-sqrt-square_binary64_7934` `rem-square-sqrt_binary64_7933` `times-frac_binary64_7927` `mul-1-neg_binary64_7913` `-inverses_binary64_7901` `+-inverses_binary64_7900` `lft-mult-inverse_binary64_7899` `rgt-mult-inverse_binary64_7898` `remove-double-div_binary64_7897` `pow-sqr_binary64_7894` `sqr-pow_binary64_7893` `difference-of-sqr--1_binary64_7892` `difference-of-sqr-1_binary64_7891` `difference-of-squares_binary64_7890` `unswap-sqr_binary64_7889` `cancel-sign-sub_binary64_7886` `distribute-neg-frac_binary64_7885` `distribute-neg-out_binary64_7883` `distribute-rgt1-in_binary64_7877` `distribute-lft1-in_binary64_7876` `distribute-rgt-out--_binary64_7875` `distribute-rgt-out_binary64_7874` `distribute-lft-out--_binary64_7873` `distribute-lft-out_binary64_7872` `count-2_binary64_7869` `associate-l/_binary64_7864` `associate-*r/_binary64_7863`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	231
1	139	231
2	310	231
3	531	231
4	801	231
5	900	231
6	1051	231
7	1759	231
8	3197	231
9	4590	231
10	5017	231
0	5	5
1	5	5

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.6%	98.2%	0.2%	10
3.1%	90.4%	6.5%	11
9.2%	84.4%	6.5%	12
13%	80.6%	6.5%	13
24.8%	68.7%	6.5%	14

Symmetry

(sort x y)

(sort t a)

Compiler

Compiled 15 to 13 computations (13.3% saved)

sample48.0ms (0.3%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
3.0ms	61×	body	128	nan
1.0ms	31×	body	128	invalid

Compiler

Compiled 29 to 30 computations (-3.4% saved)

simplify54.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

138×	`distribute-rgt-in_binary64_7871`
130×	`cancel-sign-sub-inv_binary64_7887`
128×	`associate-/r/_binary64_7867`
121×	`unsub-neg_binary64_7915`
118×	`associate-/l*_binary64_7866`
114×	`associate-l_binary64_7862`
109×	`distribute-rgt-neg-in_binary64_7879`
104×	`div-sub_binary64_7926`
97×	`distribute-lft-in_binary64_7870`
93×	`distribute-rgt-neg-out_binary64_7881`
91×	`associate-r_binary64_7861`
82×	`distribute-lft-neg-out_binary64_7880`
78×	`associate-/r*_binary64_7865`
62×	`sub-neg_binary64_7914` `distribute-lft-neg-in_binary64_7878`
59×	`*-commutative_binary64_7852`
55×	`neg-sub0_binary64_7916`
46×	`associate-/l/_binary64_7868`
39×	`mul0-rgt_binary64_7904`
38×	`neg-mul-1_binary64_7917`
35×	`mul0-lft_binary64_7903`
30×	`distribute-neg-frac_binary64_7885`
27×	`distribute-frac-neg_binary64_7884`
26×	`associate--r+_binary64_7857`
20×	`associate-*l/_binary64_7864`
19×	`remove-double-neg_binary64_7909`
18×	`*-lft-identity_binary64_7910`
17×	`+-commutative_binary64_7851`
14×	`*-rgt-identity_binary64_7911` `div0_binary64_7902`
12×	`mul-1-neg_binary64_7913` `distribute-neg-in_binary64_7882`
9×	`associate-+l-_binary64_7856`
8×	`/-rgt-identity_binary64_7912`
7×	`+-lft-identity_binary64_7905`
6×	`sub0-neg_binary64_7908`
5×	`associate-*r/_binary64_7863`
3×	`--rgt-identity_binary64_7907` `associate--r-_binary64_7860` `associate-+l+_binary64_7854`
1×	`1-exp_binary64_7965` `+-rgt-identity_binary64_7906` `swap-sqr_binary64_7888` `cancel-sign-sub_binary64_7886` `associate--l+_binary64_7858` `associate-+r-_binary64_7855` `associate-+r+_binary64_7853`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_8184` `erf-erfc_binary64_8183` `erf-odd_binary64_8182` `if-if-and-not_binary64_8181` `if-if-and_binary64_8180` `if-if-or-not_binary64_8179` `if-if-or_binary64_8178` `if-not_binary64_8177` `if-same_binary64_8176` `if-false_binary64_8175` `if-true_binary64_8174` `not-gte_binary64_8173` `not-lte_binary64_8172` `not-gt_binary64_8171` `not-lt_binary64_8170` `gte-same_binary64_8169` `lte-same_binary64_8168` `gt-same_binary64_8167` `lt-same_binary64_8166` `sinh---cosh_binary64_8113` `sinh-+-cosh_binary64_8112` `sinh-cosh_binary64_8111` `tanh-def-c_binary64_8110` `tanh-def-b_binary64_8109` `tanh-def-a_binary64_8108` `cosh-def_binary64_8107` `sinh-def_binary64_8106` `tan-neg_binary64_8053` `cos-neg_binary64_8052` `sin-neg_binary64_8051` `tan-0_binary64_8050` `cos-0_binary64_8049` `sin-0_binary64_8048` `hang-m-tan_binary64_8047` `hang-p-tan_binary64_8046` `hang-m0-tan_binary64_8045` `hang-p0-tan_binary64_8044` `hang-0m-tan_binary64_8043` `hang-0p-tan_binary64_8042` `tan-+PI/2_binary64_8041` `tan-+PI_binary64_8040` `tan-PI_binary64_8039` `tan-PI/3_binary64_8038` `tan-PI/4_binary64_8037` `tan-PI/6_binary64_8036` `cos-+PI/2_binary64_8035` `cos-+PI_binary64_8034` `cos-PI_binary64_8033` `cos-PI/2_binary64_8032` `cos-PI/3_binary64_8031` `cos-PI/4_binary64_8030` `cos-PI/6_binary64_8029` `sin-+PI/2_binary64_8028` `sin-+PI_binary64_8027` `sin-PI_binary64_8026` `sin-PI/2_binary64_8025` `sin-PI/3_binary64_8024` `sin-PI/4_binary64_8023` `sin-PI/6_binary64_8022` `sub-1-sin_binary64_8021` `sub-1-cos_binary64_8020` `-1-add-sin_binary64_8019` `-1-add-cos_binary64_8018` `1-sub-sin_binary64_8017` `1-sub-cos_binary64_8016` `cos-sin-sum_binary64_8015` `log-E_binary64_8011` `log-pow_binary64_8010` `log-rec_binary64_8009` `log-div_binary64_8008` `log-prod_binary64_8007` `pow-base-0_binary64_8005` `unpow1/3_binary64_7988` `unpow3_binary64_7987` `unpow2_binary64_7986` `unpow1/2_binary64_7985` `pow-plus_binary64_7984` `exp-to-pow_binary64_7983` `pow-base-1_binary64_7981` `unpow0_binary64_7980` `unpow1_binary64_7979` `unpow-1_binary64_7978` `exp-lft-cube_binary64_7977` `exp-lft-sqr_binary64_7976` `exp-cbrt_binary64_7975` `exp-sqrt_binary64_7974` `exp-prod_binary64_7973` `div-exp_binary64_7972` `rec-exp_binary64_7971` `prod-exp_binary64_7970` `exp-diff_binary64_7969` `exp-neg_binary64_7968` `exp-sum_binary64_7967` `e-exp-1_binary64_7966` `exp-1-e_binary64_7964` `exp-0_binary64_7963` `rem-log-exp_binary64_7962` `rem-exp-log_binary64_7961` `cube-unmult_binary64_7958` `cube-mult_binary64_7951` `cube-div_binary64_7950` `cube-prod_binary64_7949` `cube-neg_binary64_7948` `rem-3cbrt-rft_binary64_7947` `rem-3cbrt-lft_binary64_7946` `rem-cbrt-cube_binary64_7945` `rem-cube-cbrt_binary64_7944` `sqr-abs_binary64_7936` `sqr-neg_binary64_7935` `rem-sqrt-square_binary64_7934` `rem-square-sqrt_binary64_7933` `times-frac_binary64_7927` `*-inverses_binary64_7901` `+-inverses_binary64_7900` `lft-mult-inverse_binary64_7899` `rgt-mult-inverse_binary64_7898` `remove-double-div_binary64_7897` `pow-sqr_binary64_7894` `sqr-pow_binary64_7893` `difference-of-sqr--1_binary64_7892` `difference-of-sqr-1_binary64_7891` `difference-of-squares_binary64_7890` `unswap-sqr_binary64_7889` `distribute-neg-out_binary64_7883` `distribute-rgt1-in_binary64_7877` `distribute-lft1-in_binary64_7876` `distribute-rgt-out--_binary64_7875` `distribute-rgt-out_binary64_7874` `distribute-lft-out--_binary64_7873` `distribute-lft-out_binary64_7872` `count-2_binary64_7869` `associate--l-_binary64_7859`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	25	21
2	51	21
3	81	21
4	118	21
5	141	21
6	170	21
7	204	21
8	410	21
9	742	21
10	959	21
11	845	21
12	901	21
13	899	21
14	899	21
15	899	21
16	806	21

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

22.9b

Counts

1 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 z z) (.f64 t a))
6.9b	(.f64 (.f64 x y) z)
7.5b	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
21.3b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite126.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

19.8b

Rules

18×	`add-exp-log_binary64_7959` `add-cbrt-cube_binary64_7957`
11×	`add-sqr-sqrt_binary64_7943`
10×	`pow1_binary64_7982` `add-cube-cbrt_binary64_7956` `*-un-lft-identity_binary64_7921`
9×	`sqrt-prod_binary64_7937`
6×	`add-log-exp_binary64_7960` `prod-exp_binary64_7970` `cbrt-unprod_binary64_7954` `times-frac_binary64_7927` `associate-/r*_binary64_7865`
4×	`sqrt-div_binary64_7938`
3×	`flip3--_binary64_7925` `flip--_binary64_7896` `div-exp_binary64_7972` `cbrt-undiv_binary64_7955` `pow-prod-down_binary64_7992` `associate-r_binary64_7861`
2×	`associate-/r/_binary64_7867`
1×	`pow1/2_binary64_8001` `sqrt-pow1_binary64_7939` `rem-sqrt-square_binary64_7934` `frac-2neg_binary64_7932` `clear-num_binary64_7920` `div-inv_binary64_7918` `associate-/l_binary64_7866` `associate-l_binary64_7862` `-commutative_binary64_7852` `diff-log_binary64_8013` `sub-neg_binary64_7914` `cancel-sign-sub-inv_binary64_7887`

Counts

4 → 76

Calls

4 calls:

16.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
5.0ms	(.f64 (.f64 x y) z)
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 1787 to 278 computations (84.4% saved)

series1.3s (6.8%)

Error

3.1b

Counts

4 → 67

Calls

4 calls:

686.0ms	(/.f64 (.f64 (.f64 x y) z) (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
194.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
185.0ms	(-.f64 (.f64 z z) (.f64 t a))
141.0ms	(.f64 (.f64 x y) z)

Compiler

Compiled 3069 to 2142 computations (30.2% saved)

simplify106.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

524×	`associate-/r/_binary64_7867`
218×	`associate-l_binary64_7862`
215×	`associate-/l*_binary64_7866`
204×	`associate-r_binary64_7861`
180×	`times-frac_binary64_7927`
169×	`distribute-rgt-neg-in_binary64_7879`
159×	`distribute-lft-neg-in_binary64_7878`
142×	`div-sub_binary64_7926`
124×	`distribute-neg-frac_binary64_7885`
117×	`*-commutative_binary64_7852`
114×	`cancel-sign-sub-inv_binary64_7887`
88×	`cube-prod_binary64_7949` `associate-/r*_binary64_7865`
84×	`log-prod_binary64_8007`
83×	`exp-prod_binary64_7973`
73×	`associate-*l/_binary64_7864`
65×	`associate-*r/_binary64_7863`
63×	`log-div_binary64_8008`
60×	`cube-div_binary64_7950`
58×	`unswap-sqr_binary64_7889`
52×	`+-commutative_binary64_7851`
51×	`distribute-rgt-in_binary64_7871`
50×	`sqr-pow_binary64_7893`
49×	`sub-neg_binary64_7914`
48×	`neg-sub0_binary64_7916`
43×	`neg-mul-1_binary64_7917` `distribute-lft-in_binary64_7870`
38×	`associate-/l/_binary64_7868` `associate--l+_binary64_7858`
37×	`associate-+l-_binary64_7856`
36×	`associate-+l+_binary64_7854`
32×	`unpow3_binary64_7987`
29×	`associate-+r-_binary64_7855` `associate-+r+_binary64_7853`
28×	`cube-mult_binary64_7951`
21×	`*-rgt-identity_binary64_7911`
17×	`swap-sqr_binary64_7888`
15×	`/-rgt-identity_binary64_7912`
13×	`exp-sum_binary64_7967` `*-lft-identity_binary64_7910` `distribute-neg-in_binary64_7882` `distribute-lft-neg-out_binary64_7880` `distribute-rgt-out_binary64_7874` `associate--l-_binary64_7859`
12×	`cube-unmult_binary64_7958`
11×	`unsub-neg_binary64_7915`
10×	`associate--r+_binary64_7857`
9×	`mul-1-neg_binary64_7913`
8×	`log-rec_binary64_8009`
7×	`pow-plus_binary64_7984` `distribute-rgt-neg-out_binary64_7881`
6×	`exp-diff_binary64_7969` `rem-sqrt-square_binary64_7934`
5×	`pow-sqr_binary64_7894` `difference-of-squares_binary64_7890`
4×	`unpow1/2_binary64_7985` `distribute-lft-out_binary64_7872`
3×	`unpow2_binary64_7986` `unpow1_binary64_7979`
2×	`log-pow_binary64_8010` `rem-square-sqrt_binary64_7933`
1×	`div-exp_binary64_7972` `1-exp_binary64_7965` `exp-1-e_binary64_7964` `sqr-neg_binary64_7935` `+-rgt-identity_binary64_7906` `count-2_binary64_7869`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_8184` `erf-erfc_binary64_8183` `erf-odd_binary64_8182` `if-if-and-not_binary64_8181` `if-if-and_binary64_8180` `if-if-or-not_binary64_8179` `if-if-or_binary64_8178` `if-not_binary64_8177` `if-same_binary64_8176` `if-false_binary64_8175` `if-true_binary64_8174` `not-gte_binary64_8173` `not-lte_binary64_8172` `not-gt_binary64_8171` `not-lt_binary64_8170` `gte-same_binary64_8169` `lte-same_binary64_8168` `gt-same_binary64_8167` `lt-same_binary64_8166` `sinh---cosh_binary64_8113` `sinh-+-cosh_binary64_8112` `sinh-cosh_binary64_8111` `tanh-def-c_binary64_8110` `tanh-def-b_binary64_8109` `tanh-def-a_binary64_8108` `cosh-def_binary64_8107` `sinh-def_binary64_8106` `tan-neg_binary64_8053` `cos-neg_binary64_8052` `sin-neg_binary64_8051` `tan-0_binary64_8050` `cos-0_binary64_8049` `sin-0_binary64_8048` `hang-m-tan_binary64_8047` `hang-p-tan_binary64_8046` `hang-m0-tan_binary64_8045` `hang-p0-tan_binary64_8044` `hang-0m-tan_binary64_8043` `hang-0p-tan_binary64_8042` `tan-+PI/2_binary64_8041` `tan-+PI_binary64_8040` `tan-PI_binary64_8039` `tan-PI/3_binary64_8038` `tan-PI/4_binary64_8037` `tan-PI/6_binary64_8036` `cos-+PI/2_binary64_8035` `cos-+PI_binary64_8034` `cos-PI_binary64_8033` `cos-PI/2_binary64_8032` `cos-PI/3_binary64_8031` `cos-PI/4_binary64_8030` `cos-PI/6_binary64_8029` `sin-+PI/2_binary64_8028` `sin-+PI_binary64_8027` `sin-PI_binary64_8026` `sin-PI/2_binary64_8025` `sin-PI/3_binary64_8024` `sin-PI/4_binary64_8023` `sin-PI/6_binary64_8022` `sub-1-sin_binary64_8021` `sub-1-cos_binary64_8020` `-1-add-sin_binary64_8019` `-1-add-cos_binary64_8018` `1-sub-sin_binary64_8017` `1-sub-cos_binary64_8016` `cos-sin-sum_binary64_8015` `log-E_binary64_8011` `pow-base-0_binary64_8005` `unpow1/3_binary64_7988` `exp-to-pow_binary64_7983` `pow-base-1_binary64_7981` `unpow0_binary64_7980` `unpow-1_binary64_7978` `exp-lft-cube_binary64_7977` `exp-lft-sqr_binary64_7976` `exp-cbrt_binary64_7975` `exp-sqrt_binary64_7974` `rec-exp_binary64_7971` `prod-exp_binary64_7970` `exp-neg_binary64_7968` `e-exp-1_binary64_7966` `exp-0_binary64_7963` `rem-log-exp_binary64_7962` `rem-exp-log_binary64_7961` `cube-neg_binary64_7948` `rem-3cbrt-rft_binary64_7947` `rem-3cbrt-lft_binary64_7946` `rem-cbrt-cube_binary64_7945` `rem-cube-cbrt_binary64_7944` `sqr-abs_binary64_7936` `remove-double-neg_binary64_7909` `sub0-neg_binary64_7908` `--rgt-identity_binary64_7907` `+-lft-identity_binary64_7905` `mul0-rgt_binary64_7904` `mul0-lft_binary64_7903` `div0_binary64_7902` `*-inverses_binary64_7901` `+-inverses_binary64_7900` `lft-mult-inverse_binary64_7899` `rgt-mult-inverse_binary64_7898` `remove-double-div_binary64_7897` `difference-of-sqr--1_binary64_7892` `difference-of-sqr-1_binary64_7891` `cancel-sign-sub_binary64_7886` `distribute-frac-neg_binary64_7884` `distribute-neg-out_binary64_7883` `distribute-rgt1-in_binary64_7877` `distribute-lft1-in_binary64_7876` `distribute-rgt-out--_binary64_7875` `distribute-lft-out--_binary64_7873` `associate--r-_binary64_7860`

Counts

143 → 91

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	206	2590
1	540	2330
2	2392	2330
3	4563	2330
4	5103	2330

prune97.0ms (0.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	81	10	91
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	11	92

Error

4.1b

Counts

92 → 11

Compiler

Compiled 1866 to 459 computations (75.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
0.8b	(-.f64 (.f64 z z) (.f64 t a))
5.2b	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
21.3b	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite152.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

36×	`times-frac_binary64_7927`
34×	`add-sqr-sqrt_binary64_7943`
33×	`add-cube-cbrt_binary64_7956` `*-un-lft-identity_binary64_7921`
24×	`sqrt-prod_binary64_7937` `associate-r_binary64_7861`
18×	`add-exp-log_binary64_7959` `add-cbrt-cube_binary64_7957`
10×	`pow1_binary64_7982`
6×	`add-log-exp_binary64_7960` `sqrt-div_binary64_7938` `prod-exp_binary64_7970` `cbrt-unprod_binary64_7954` `associate-/r*_binary64_7865`
4×	`flip3--_binary64_7925` `flip--_binary64_7896` `associate-/r/_binary64_7867`
3×	`pow-prod-down_binary64_7992` `div-exp_binary64_7972` `cbrt-undiv_binary64_7955` `associate-/l*_binary64_7866`
2×	`div-inv_binary64_7918`
1×	`pow1/2_binary64_8001` `sqrt-pow1_binary64_7939` `rem-sqrt-square_binary64_7934` `associate-r/_binary64_7863` `associate-l_binary64_7862` `-commutative_binary64_7852` `diff-log_binary64_8013` `sub-neg_binary64_7914` `cancel-sign-sub-inv_binary64_7887` `frac-2neg_binary64_7932` `clear-num_binary64_7920`

Counts

4 → 112

Calls

4 calls:

14.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
7.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
4.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 2928 to 440 computations (85% saved)

series1.4s (7.5%)

Error

3.1b

Counts

4 → 73

Calls

4 calls:

696.0ms	(.f64 (.f64 x y) (/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))
261.0ms	(/.f64 z (sqrt.f64 (-.f64 (.f64 z z) (.f64 t a))))
190.0ms	(sqrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
178.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 3463 to 2557 computations (26.2% saved)

simplify223.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

420×	`associate-/r/_binary64_7867`
284×	`associate-/l/_binary64_7868`
280×	`associate-l_binary64_7862`
261×	`associate-r_binary64_7861`
224×	`distribute-rgt-neg-in_binary64_7879`
210×	`distribute-lft-neg-in_binary64_7878`
178×	`times-frac_binary64_7927`
176×	`*-commutative_binary64_7852`
174×	`distribute-neg-frac_binary64_7885`
173×	`associate-/l*_binary64_7866`
130×	`cancel-sign-sub-inv_binary64_7887`
128×	`associate-*r/_binary64_7863`
93×	`associate-/r*_binary64_7865`
75×	`associate-*l/_binary64_7864`
72×	`exp-prod_binary64_7973`
65×	`neg-sub0_binary64_7916`
61×	`distribute-rgt-in_binary64_7871`
59×	`neg-mul-1_binary64_7917`
55×	`log-prod_binary64_8007` `sub-neg_binary64_7914`
52×	`unswap-sqr_binary64_7889`
48×	`sqr-pow_binary64_7893`
46×	`distribute-lft-in_binary64_7870`
36×	`+-commutative_binary64_7851`
31×	`*-rgt-identity_binary64_7911`
29×	`log-div_binary64_8008`
25×	`cube-div_binary64_7950` `*-lft-identity_binary64_7910`
22×	`unpow3_binary64_7987` `distribute-neg-in_binary64_7882`
19×	`cube-prod_binary64_7949` `swap-sqr_binary64_7888`
17×	`cube-mult_binary64_7951`
14×	`associate-+l+_binary64_7854`
13×	`distribute-lft-neg-out_binary64_7880` `distribute-rgt-out_binary64_7874`
12×	`cube-unmult_binary64_7958` `unsub-neg_binary64_7915`
11×	`mul-1-neg_binary64_7913`
10×	`associate--r+_binary64_7857` `associate-+r+_binary64_7853`
9×	`pow-plus_binary64_7984` `exp-sum_binary64_7967`
8×	`div-sub_binary64_7926`
7×	`/-rgt-identity_binary64_7912` `associate-+r-_binary64_7855`
5×	`exp-diff_binary64_7969` `pow-sqr_binary64_7894` `difference-of-squares_binary64_7890` `distribute-rgt-neg-out_binary64_7881` `associate--l+_binary64_7858`
4×	`unpow1/2_binary64_7985` `rem-sqrt-square_binary64_7934` `+-rgt-identity_binary64_7906` `distribute-lft-out_binary64_7872`
3×	`log-pow_binary64_8010` `unpow2_binary64_7986` `unpow1_binary64_7979`
2×	`exp-neg_binary64_7968` `rem-square-sqrt_binary64_7933`
1×	`pow-base-1_binary64_7981` `div-exp_binary64_7972` `1-exp_binary64_7965` `exp-1-e_binary64_7964` `distribute-neg-out_binary64_7883` `count-2_binary64_7869` `associate-+l-_binary64_7856`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_8184` `erf-erfc_binary64_8183` `erf-odd_binary64_8182` `if-if-and-not_binary64_8181` `if-if-and_binary64_8180` `if-if-or-not_binary64_8179` `if-if-or_binary64_8178` `if-not_binary64_8177` `if-same_binary64_8176` `if-false_binary64_8175` `if-true_binary64_8174` `not-gte_binary64_8173` `not-lte_binary64_8172` `not-gt_binary64_8171` `not-lt_binary64_8170` `gte-same_binary64_8169` `lte-same_binary64_8168` `gt-same_binary64_8167` `lt-same_binary64_8166` `sinh---cosh_binary64_8113` `sinh-+-cosh_binary64_8112` `sinh-cosh_binary64_8111` `tanh-def-c_binary64_8110` `tanh-def-b_binary64_8109` `tanh-def-a_binary64_8108` `cosh-def_binary64_8107` `sinh-def_binary64_8106` `tan-neg_binary64_8053` `cos-neg_binary64_8052` `sin-neg_binary64_8051` `tan-0_binary64_8050` `cos-0_binary64_8049` `sin-0_binary64_8048` `hang-m-tan_binary64_8047` `hang-p-tan_binary64_8046` `hang-m0-tan_binary64_8045` `hang-p0-tan_binary64_8044` `hang-0m-tan_binary64_8043` `hang-0p-tan_binary64_8042` `tan-+PI/2_binary64_8041` `tan-+PI_binary64_8040` `tan-PI_binary64_8039` `tan-PI/3_binary64_8038` `tan-PI/4_binary64_8037` `tan-PI/6_binary64_8036` `cos-+PI/2_binary64_8035` `cos-+PI_binary64_8034` `cos-PI_binary64_8033` `cos-PI/2_binary64_8032` `cos-PI/3_binary64_8031` `cos-PI/4_binary64_8030` `cos-PI/6_binary64_8029` `sin-+PI/2_binary64_8028` `sin-+PI_binary64_8027` `sin-PI_binary64_8026` `sin-PI/2_binary64_8025` `sin-PI/3_binary64_8024` `sin-PI/4_binary64_8023` `sin-PI/6_binary64_8022` `sub-1-sin_binary64_8021` `sub-1-cos_binary64_8020` `-1-add-sin_binary64_8019` `-1-add-cos_binary64_8018` `1-sub-sin_binary64_8017` `1-sub-cos_binary64_8016` `cos-sin-sum_binary64_8015` `log-E_binary64_8011` `log-rec_binary64_8009` `pow-base-0_binary64_8005` `unpow1/3_binary64_7988` `exp-to-pow_binary64_7983` `unpow0_binary64_7980` `unpow-1_binary64_7978` `exp-lft-cube_binary64_7977` `exp-lft-sqr_binary64_7976` `exp-cbrt_binary64_7975` `exp-sqrt_binary64_7974` `rec-exp_binary64_7971` `prod-exp_binary64_7970` `e-exp-1_binary64_7966` `exp-0_binary64_7963` `rem-log-exp_binary64_7962` `rem-exp-log_binary64_7961` `cube-neg_binary64_7948` `rem-3cbrt-rft_binary64_7947` `rem-3cbrt-lft_binary64_7946` `rem-cbrt-cube_binary64_7945` `rem-cube-cbrt_binary64_7944` `sqr-abs_binary64_7936` `sqr-neg_binary64_7935` `remove-double-neg_binary64_7909` `sub0-neg_binary64_7908` `--rgt-identity_binary64_7907` `+-lft-identity_binary64_7905` `mul0-rgt_binary64_7904` `mul0-lft_binary64_7903` `div0_binary64_7902` `*-inverses_binary64_7901` `+-inverses_binary64_7900` `lft-mult-inverse_binary64_7899` `rgt-mult-inverse_binary64_7898` `remove-double-div_binary64_7897` `difference-of-sqr--1_binary64_7892` `difference-of-sqr-1_binary64_7891` `cancel-sign-sub_binary64_7886` `distribute-frac-neg_binary64_7884` `distribute-rgt1-in_binary64_7877` `distribute-lft1-in_binary64_7876` `distribute-rgt-out--_binary64_7875` `distribute-lft-out--_binary64_7873` `associate--r-_binary64_7860` `associate--l-_binary64_7859`

Counts

185 → 107

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	254	3864
1	665	3537
2	2712	3537
3	4876	3537
4	4987	3537
5	4999	3537
6	5000	3537
7	4979	3537

prune110.0ms (0.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	4	5	9
Picked	0	1	1
Done	0	1	1
Total	108	10	118

Error

3.4b

Counts

118 → 10

Compiler

Compiled 2185 to 538 computations (75.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 z z) (.f64 t a))
5.2b	(.f64 (.f64 x y) (.f64 (/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 (cbrt.f64 z) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
22.2b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
22.2b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite186.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

3.4b

Rules

69×	`add-exp-log_binary64_7959`
55×	`add-cbrt-cube_binary64_7957`
37×	`prod-exp_binary64_7970` `cbrt-unprod_binary64_7954`
16×	`pow1_binary64_7982`
14×	`div-exp_binary64_7972` `cbrt-undiv_binary64_7955`
8×	`pow-prod-down_binary64_7992`
6×	`add-log-exp_binary64_7960` `add-cube-cbrt_binary64_7956` `cbrt-prod_binary64_7952` `add-sqr-sqrt_binary64_7943` `*-un-lft-identity_binary64_7921`
4×	`cbrt-div_binary64_7953` `associate-*r/_binary64_7863`
3×	`flip3--_binary64_7925` `flip--_binary64_7896`
2×	`pow1/3_binary64_8003`
1×	`frac-times_binary64_7931` `associate-l/_binary64_7864` `associate-l_binary64_7862` `associate-r_binary64_7861` `-commutative_binary64_7852` `diff-log_binary64_8013` `sub-neg_binary64_7914` `cancel-sign-sub-inv_binary64_7887`

Counts

4 → 83

Calls

4 calls:

22.0ms	(.f64 (.f64 x y) (.f64 (/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 (cbrt.f64 z) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
4.0ms	(-.f64 (.f64 z z) (.f64 t a))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 4145 to 407 computations (90.2% saved)

series2.8s (15.3%)

Error

3.4b

Counts

4 → 83

Calls

4 calls:

1.5s	(.f64 (.f64 x y) (.f64 (/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a))))) (/.f64 (cbrt.f64 z) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
499.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
473.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
195.0ms	(-.f64 (.f64 z z) (.f64 t a))

Compiler

Compiled 9551 to 6269 computations (34.4% saved)

simplify189.0ms (1%)

Algorithm

1×	egg-herbie

Rules

447×	`associate-l_binary64_7862`
435×	`associate-r_binary64_7861`
353×	`unswap-sqr_binary64_7889`
228×	`*-commutative_binary64_7852`
214×	`times-frac_binary64_7927`
195×	`associate-/l*_binary64_7866`
165×	`log-prod_binary64_8007`
164×	`associate-*r/_binary64_7863`
148×	`associate-/r*_binary64_7865`
130×	`associate-*l/_binary64_7864`
112×	`sqr-pow_binary64_7893`
94×	`exp-prod_binary64_7973`
92×	`sub-neg_binary64_7914`
62×	`swap-sqr_binary64_7888`
55×	`neg-sub0_binary64_7916`
54×	`log-div_binary64_8008`
51×	`neg-mul-1_binary64_7917`
48×	`+-commutative_binary64_7851`
38×	`cube-prod_binary64_7949`
33×	`exp-sum_binary64_7967`
31×	`cancel-sign-sub-inv_binary64_7887`
24×	`associate-+r+_binary64_7853`
23×	`associate-+l+_binary64_7854`
22×	`distribute-rgt-neg-in_binary64_7879`
20×	`unsub-neg_binary64_7915`
19×	`distribute-lft-neg-in_binary64_7878`
17×	`exp-diff_binary64_7969` `cube-unmult_binary64_7958` `associate-/r/_binary64_7867`
16×	`log-pow_binary64_8010` `pow-sqr_binary64_7894`
14×	`div-sub_binary64_7926` `associate-+r-_binary64_7855`
13×	`cube-div_binary64_7950`
12×	`unpow1/3_binary64_7988` `mul-1-neg_binary64_7913` `associate-+l-_binary64_7856`
11×	`distribute-rgt-in_binary64_7871` `distribute-lft-in_binary64_7870`
9×	`rem-sqrt-square_binary64_7934`
8×	`unpow3_binary64_7987` `pow-plus_binary64_7984` `associate--r+_binary64_7857`
7×	`cube-mult_binary64_7951`
6×	`distribute-neg-in_binary64_7882`
5×	`difference-of-squares_binary64_7890` `associate--r-_binary64_7860`
4×	`exp-to-pow_binary64_7983` `exp-neg_binary64_7968` `distribute-lft-neg-out_binary64_7880` `associate--l+_binary64_7858`
3×	`unpow2_binary64_7986` `unpow1/2_binary64_7985` `unpow1_binary64_7979` `distribute-neg-frac_binary64_7885` `distribute-rgt-out_binary64_7874`
2×	`log-rec_binary64_8009` `rem-3cbrt-lft_binary64_7946` `remove-double-neg_binary64_7909` `distribute-rgt-neg-out_binary64_7881` `associate-/l/_binary64_7868`
1×	`div-exp_binary64_7972` `1-exp_binary64_7965` `rem-cbrt-cube_binary64_7945` `rem-cube-cbrt_binary64_7944` `sqr-abs_binary64_7936` `rem-square-sqrt_binary64_7933` `+-rgt-identity_binary64_7906` `count-2_binary64_7869`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_8184` `erf-erfc_binary64_8183` `erf-odd_binary64_8182` `if-if-and-not_binary64_8181` `if-if-and_binary64_8180` `if-if-or-not_binary64_8179` `if-if-or_binary64_8178` `if-not_binary64_8177` `if-same_binary64_8176` `if-false_binary64_8175` `if-true_binary64_8174` `not-gte_binary64_8173` `not-lte_binary64_8172` `not-gt_binary64_8171` `not-lt_binary64_8170` `gte-same_binary64_8169` `lte-same_binary64_8168` `gt-same_binary64_8167` `lt-same_binary64_8166` `sinh---cosh_binary64_8113` `sinh-+-cosh_binary64_8112` `sinh-cosh_binary64_8111` `tanh-def-c_binary64_8110` `tanh-def-b_binary64_8109` `tanh-def-a_binary64_8108` `cosh-def_binary64_8107` `sinh-def_binary64_8106` `tan-neg_binary64_8053` `cos-neg_binary64_8052` `sin-neg_binary64_8051` `tan-0_binary64_8050` `cos-0_binary64_8049` `sin-0_binary64_8048` `hang-m-tan_binary64_8047` `hang-p-tan_binary64_8046` `hang-m0-tan_binary64_8045` `hang-p0-tan_binary64_8044` `hang-0m-tan_binary64_8043` `hang-0p-tan_binary64_8042` `tan-+PI/2_binary64_8041` `tan-+PI_binary64_8040` `tan-PI_binary64_8039` `tan-PI/3_binary64_8038` `tan-PI/4_binary64_8037` `tan-PI/6_binary64_8036` `cos-+PI/2_binary64_8035` `cos-+PI_binary64_8034` `cos-PI_binary64_8033` `cos-PI/2_binary64_8032` `cos-PI/3_binary64_8031` `cos-PI/4_binary64_8030` `cos-PI/6_binary64_8029` `sin-+PI/2_binary64_8028` `sin-+PI_binary64_8027` `sin-PI_binary64_8026` `sin-PI/2_binary64_8025` `sin-PI/3_binary64_8024` `sin-PI/4_binary64_8023` `sin-PI/6_binary64_8022` `sub-1-sin_binary64_8021` `sub-1-cos_binary64_8020` `-1-add-sin_binary64_8019` `-1-add-cos_binary64_8018` `1-sub-sin_binary64_8017` `1-sub-cos_binary64_8016` `cos-sin-sum_binary64_8015` `log-E_binary64_8011` `pow-base-0_binary64_8005` `pow-base-1_binary64_7981` `unpow0_binary64_7980` `unpow-1_binary64_7978` `exp-lft-cube_binary64_7977` `exp-lft-sqr_binary64_7976` `exp-cbrt_binary64_7975` `exp-sqrt_binary64_7974` `rec-exp_binary64_7971` `prod-exp_binary64_7970` `e-exp-1_binary64_7966` `exp-1-e_binary64_7964` `exp-0_binary64_7963` `rem-log-exp_binary64_7962` `rem-exp-log_binary64_7961` `cube-neg_binary64_7948` `rem-3cbrt-rft_binary64_7947` `sqr-neg_binary64_7935` `/-rgt-identity_binary64_7912` `-rgt-identity_binary64_7911` `-lft-identity_binary64_7910` `sub0-neg_binary64_7908` `--rgt-identity_binary64_7907` `+-lft-identity_binary64_7905` `mul0-rgt_binary64_7904` `mul0-lft_binary64_7903` `div0_binary64_7902` `*-inverses_binary64_7901` `+-inverses_binary64_7900` `lft-mult-inverse_binary64_7899` `rgt-mult-inverse_binary64_7898` `remove-double-div_binary64_7897` `difference-of-sqr--1_binary64_7892` `difference-of-sqr-1_binary64_7891` `cancel-sign-sub_binary64_7886` `distribute-frac-neg_binary64_7884` `distribute-neg-out_binary64_7883` `distribute-rgt1-in_binary64_7877` `distribute-lft1-in_binary64_7876` `distribute-rgt-out--_binary64_7875` `distribute-lft-out--_binary64_7873` `distribute-lft-out_binary64_7872` `associate--l-_binary64_7859`

Counts

166 → 139

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	6550
1	847	5238
2	3515	5210
3	4948	5210
4	5052	5210

prune199.0ms (1.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	137	12	149

Error

3.4b

Counts

149 → 12

Compiler

Compiled 5252 to 1133 computations (78.4% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.3b	(.f64 y (/.f64 z (.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
2.3b	(.f64 x (.f64 y (/.f64 z (.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))))
22.2b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
22.2b	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

rewrite143.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

3.4b

Rules

27×	`add-exp-log_binary64_7959` `add-cbrt-cube_binary64_7957`
12×	`add-sqr-sqrt_binary64_7943` `prod-exp_binary64_7970` `cbrt-unprod_binary64_7954`
11×	`pow1_binary64_7982`
10×	`add-cube-cbrt_binary64_7956` `-un-lft-identity_binary64_7921` `associate-r*_binary64_7861`
6×	`cbrt-div_binary64_7953` `cbrt-prod_binary64_7952` `associate-l_binary64_7862`
4×	`add-log-exp_binary64_7960` `pow-prod-down_binary64_7992` `div-exp_binary64_7972` `cbrt-undiv_binary64_7955`
3×	`flip3--_binary64_7925` `flip--_binary64_7896` `associate-*r/_binary64_7863` `times-frac_binary64_7927`
2×	`pow1/3_binary64_8003` `-commutative_binary64_7852` `sqrt-div_binary64_7938` `associate-l/_binary64_7864` `associate-/r/_binary64_7867`
1×	`unswap-sqr_binary64_7889` `div-inv_binary64_7918`

Counts

4 → 78

Calls

4 calls:

13.0ms	(.f64 x (.f64 y (/.f64 z (.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))))
13.0ms	(.f64 y (/.f64 z (.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
4.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 3093 to 399 computations (87.1% saved)

series3.6s (19.1%)

Error

3.4b

Counts

4 → 83

Calls

4 calls:

1.5s	(.f64 x (.f64 y (/.f64 z (.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (*.f64 t a))))))))
981.0ms	(.f64 y (/.f64 z (.f64 (sqrt.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))) (fabs.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))))))
506.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))
443.0ms	(cbrt.f64 (-.f64 (.f64 z z) (.f64 t a)))

Compiler

Compiled 9576 to 7025 computations (26.6% saved)

simplify154.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

407×	`associate-r_binary64_7861`
375×	`times-frac_binary64_7927`
355×	`associate-l_binary64_7862`
252×	`associate-/l*_binary64_7866`
247×	`associate-/r*_binary64_7865`
239×	`*-commutative_binary64_7852`
206×	`cancel-sign-sub-inv_binary64_7887`
154×	`associate-*r/_binary64_7863`
136×	`unswap-sqr_binary64_7889`
107×	`associate-*l/_binary64_7864`
94×	`sqr-pow_binary64_7893`
86×	`sub-neg_binary64_7914`
82×	`distribute-neg-frac_binary64_7885`
54×	`log-prod_binary64_8007`
52×	`+-commutative_binary64_7851`
49×	`neg-sub0_binary64_7916`
48×	`exp-prod_binary64_7973`
47×	`neg-mul-1_binary64_7917`
30×	`exp-sum_binary64_7967`
25×	`*-rgt-identity_binary64_7911` `associate-/r/_binary64_7867`
22×	`unsub-neg_binary64_7915`
21×	`*-lft-identity_binary64_7910` `distribute-rgt-neg-in_binary64_7879`
20×	`swap-sqr_binary64_7888`
19×	`cube-prod_binary64_7949`
18×	`div-sub_binary64_7926` `distribute-lft-neg-in_binary64_7878`
17×	`log-div_binary64_8008`
14×	`exp-diff_binary64_7969`
13×	`associate-+r+_binary64_7853`
12×	`unpow1/3_binary64_7988` `cube-unmult_binary64_7958`
11×	`cube-div_binary64_7950` `pow-sqr_binary64_7894` `associate--r+_binary64_7857` `associate-+l+_binary64_7854`
10×	`distribute-rgt-in_binary64_7871` `distribute-lft-in_binary64_7870` `associate-+r-_binary64_7855`
9×	`rem-sqrt-square_binary64_7934`
8×	`distribute-neg-in_binary64_7882`
7×	`associate-+l-_binary64_7856`
6×	`log-pow_binary64_8010`
5×	`unpow3_binary64_7987` `cube-mult_binary64_7951` `difference-of-squares_binary64_7890`
4×	`exp-to-pow_binary64_7983` `exp-neg_binary64_7968` `distribute-lft-neg-out_binary64_7880` `associate--r-_binary64_7860`
3×	`unpow2_binary64_7986` `unpow1/2_binary64_7985` `pow-plus_binary64_7984` `unpow1_binary64_7979` `mul-1-neg_binary64_7913` `distribute-rgt-out_binary64_7874`
2×	`log-rec_binary64_8009` `/-rgt-identity_binary64_7912` `remove-double-neg_binary64_7909` `distribute-rgt-neg-out_binary64_7881` `associate--l+_binary64_7858`
1×	`1-exp_binary64_7965` `exp-1-e_binary64_7964` `rem-3cbrt-lft_binary64_7946` `sqr-abs_binary64_7936` `rem-square-sqrt_binary64_7933`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_8184` `erf-erfc_binary64_8183` `erf-odd_binary64_8182` `if-if-and-not_binary64_8181` `if-if-and_binary64_8180` `if-if-or-not_binary64_8179` `if-if-or_binary64_8178` `if-not_binary64_8177` `if-same_binary64_8176` `if-false_binary64_8175` `if-true_binary64_8174` `not-gte_binary64_8173` `not-lte_binary64_8172` `not-gt_binary64_8171` `not-lt_binary64_8170` `gte-same_binary64_8169` `lte-same_binary64_8168` `gt-same_binary64_8167` `lt-same_binary64_8166` `sinh---cosh_binary64_8113` `sinh-+-cosh_binary64_8112` `sinh-cosh_binary64_8111` `tanh-def-c_binary64_8110` `tanh-def-b_binary64_8109` `tanh-def-a_binary64_8108` `cosh-def_binary64_8107` `sinh-def_binary64_8106` `tan-neg_binary64_8053` `cos-neg_binary64_8052` `sin-neg_binary64_8051` `tan-0_binary64_8050` `cos-0_binary64_8049` `sin-0_binary64_8048` `hang-m-tan_binary64_8047` `hang-p-tan_binary64_8046` `hang-m0-tan_binary64_8045` `hang-p0-tan_binary64_8044` `hang-0m-tan_binary64_8043` `hang-0p-tan_binary64_8042` `tan-+PI/2_binary64_8041` `tan-+PI_binary64_8040` `tan-PI_binary64_8039` `tan-PI/3_binary64_8038` `tan-PI/4_binary64_8037` `tan-PI/6_binary64_8036` `cos-+PI/2_binary64_8035` `cos-+PI_binary64_8034` `cos-PI_binary64_8033` `cos-PI/2_binary64_8032` `cos-PI/3_binary64_8031` `cos-PI/4_binary64_8030` `cos-PI/6_binary64_8029` `sin-+PI/2_binary64_8028` `sin-+PI_binary64_8027` `sin-PI_binary64_8026` `sin-PI/2_binary64_8025` `sin-PI/3_binary64_8024` `sin-PI/4_binary64_8023` `sin-PI/6_binary64_8022` `sub-1-sin_binary64_8021` `sub-1-cos_binary64_8020` `-1-add-sin_binary64_8019` `-1-add-cos_binary64_8018` `1-sub-sin_binary64_8017` `1-sub-cos_binary64_8016` `cos-sin-sum_binary64_8015` `log-E_binary64_8011` `pow-base-0_binary64_8005` `pow-base-1_binary64_7981` `unpow0_binary64_7980` `unpow-1_binary64_7978` `exp-lft-cube_binary64_7977` `exp-lft-sqr_binary64_7976` `exp-cbrt_binary64_7975` `exp-sqrt_binary64_7974` `div-exp_binary64_7972` `rec-exp_binary64_7971` `prod-exp_binary64_7970` `e-exp-1_binary64_7966` `exp-0_binary64_7963` `rem-log-exp_binary64_7962` `rem-exp-log_binary64_7961` `cube-neg_binary64_7948` `rem-3cbrt-rft_binary64_7947` `rem-cbrt-cube_binary64_7945` `rem-cube-cbrt_binary64_7944` `sqr-neg_binary64_7935` `sub0-neg_binary64_7908` `--rgt-identity_binary64_7907` `+-rgt-identity_binary64_7906` `+-lft-identity_binary64_7905` `mul0-rgt_binary64_7904` `mul0-lft_binary64_7903` `div0_binary64_7902` `*-inverses_binary64_7901` `+-inverses_binary64_7900` `lft-mult-inverse_binary64_7899` `rgt-mult-inverse_binary64_7898` `remove-double-div_binary64_7897` `difference-of-sqr--1_binary64_7892` `difference-of-sqr-1_binary64_7891` `cancel-sign-sub_binary64_7886` `distribute-frac-neg_binary64_7884` `distribute-neg-out_binary64_7883` `distribute-rgt1-in_binary64_7877` `distribute-lft1-in_binary64_7876` `distribute-rgt-out--_binary64_7875` `distribute-lft-out--_binary64_7873` `distribute-lft-out_binary64_7872` `count-2_binary64_7869` `associate-/l/_binary64_7868` `associate--l-_binary64_7859`

Counts

161 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	338	6791
1	910	5989
2	3810	5961
3	4967	5961

prune185.0ms (1%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	134	12	146

Error

3.4b

Counts

146 → 12

Compiler

Compiled 4779 to 1251 computations (73.8% saved)

regimes2.7s (14.7%)

Accuracy

Total 3.8b remaining (53.1%)

Threshold costs 0b (0%)

Compiler

Compiled 18940 to 12550 computations (33.7% saved)

bsearch159.0ms (0.9%)

Steps

Iters	Range	Point
9	1.2771236578840967e+58	2.2535882797895796e+64	2.8243032036053995e+60
10	-6.498500407001651e-306	1.6211506045353083e-300	7.0143619415122286e-304
8	-2.762149146957008e+75	-3.468316908599431e+71	-2.705239368116784e+72

Iters

Range

Point

1.2771236578840967e+58

2.2535882797895796e+64

2.8243032036053995e+60

-6.498500407001651e-306

1.6211506045353083e-300

7.0143619415122286e-304

-2.762149146957008e+75

-3.468316908599431e+71

-2.705239368116784e+72

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify61.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64_7852`
7×	`sub-neg_binary64_7914` `+-commutative_binary64_7851`
6×	`neg-sub0_binary64_7916`
5×	`neg-mul-1_binary64_7917`
4×	`distribute-rgt-neg-in_binary64_7879`
3×	`distribute-lft-neg-in_binary64_7878`
2×	`cancel-sign-sub-inv_binary64_7887`
1×	`1-exp_binary64_7965` `mul-1-neg_binary64_7913` `distribute-lft-neg-out_binary64_7880`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64_8181` `if-if-and_binary64_8180` `if-if-or-not_binary64_8179` `if-if-or_binary64_8178` `if-not_binary64_8177` `if-same_binary64_8176` `if-false_binary64_8175` `if-true_binary64_8174` `tan-0_binary64_8050` `cos-0_binary64_8049` `sin-0_binary64_8048` `unpow1_binary64_7979` `e-exp-1_binary64_7966` `exp-1-e_binary64_7964` `exp-0_binary64_7963` `sqr-abs_binary64_7936` `sqr-neg_binary64_7935` `unsub-neg_binary64_7915` `/-rgt-identity_binary64_7912` `-rgt-identity_binary64_7911` `-lft-identity_binary64_7910` `remove-double-neg_binary64_7909` `sub0-neg_binary64_7908` `--rgt-identity_binary64_7907` `+-rgt-identity_binary64_7906` `+-lft-identity_binary64_7905` `cancel-sign-sub_binary64_7886` `distribute-neg-frac_binary64_7885` `distribute-frac-neg_binary64_7884` `distribute-neg-out_binary64_7883` `distribute-neg-in_binary64_7882` `distribute-rgt-neg-out_binary64_7881`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	104
1	55	104
2	70	104
3	81	104
4	90	104
5	93	104
6	92	104

Remove

(sort t a)

Compiler

Compiled 408 to 210 computations (48.5% saved)

end0.0ms (0%)

sample2.9s (15.5%)

Algorithm

1×

intervals

Results

427.0ms	8000×	body	128	valid
97.0ms	2142×	body	128	nan
41.0ms	845×	body	128	invalid

Compiler

Compiled 2264 to 1496 computations (33.9% saved)

Iter	Nodes	Cost
0	13	21
1	25	21
2	51	21
3	81	21
4	118	21
5	141	21
6	170	21
7	204	21
8	410	21
9	742	21
10	959	21
11	845	21
12	901	21
13	899	21
14	899	21
15	899	21
16	806	21

Iter	Nodes	Cost
0	13	21
1	25	21
2	51	21
3	81	21
4	118	21
5	141	21
6	170	21
7	204	21
8	410	21
9	742	21
10	959	21
11	845	21
12	901	21
13	899	21
14	899	21
15	899	21
16	806	21

Details

analyze1.7s (9.2%)

sample48.0ms (0.3%)

simplify54.0ms (0.3%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite126.0ms (0.7%)

series1.3s (6.8%)

simplify106.0ms (0.6%)

prune97.0ms (0.5%)

localize10.0ms (0.1%)

rewrite152.0ms (0.8%)

series1.4s (7.5%)

simplify223.0ms (1.2%)

prune110.0ms (0.6%)

localize17.0ms (0.1%)

rewrite186.0ms (1%)

series2.8s (15.3%)

simplify189.0ms (1%)

prune199.0ms (1.1%)

localize14.0ms (0.1%)

rewrite143.0ms (0.8%)

series3.6s (19.1%)

simplify154.0ms (0.8%)

prune185.0ms (1%)

regimes2.7s (14.7%)

bsearch159.0ms (0.9%)

simplify61.0ms (0.3%)

end0.0ms (0%)

sample2.9s (15.5%)

Profiling

Iter	Nodes	Cost
0	13	21
1	25	21
2	51	21
3	81	21
4	118	21
5	141	21
6	170	21
7	204	21
8	410	21
9	742	21
10	959	21
11	845	21
12	901	21
13	899	21
14	899	21
15	899	21
16	806	21