Details

analyze353.0ms (15.8%)

Algorithm

1×	search
2×	egg-herbie

Rules

103×	`cancel-sign-sub-inv_binary64`
94×	`associate-r_binary64`
80×	`associate-l_binary64`
64×	`sub-neg_binary64`
63×	`distribute-rgt-in_binary64`
48×	`unsub-neg_binary64` `distribute-lft-in_binary64`
43×	`distribute-rgt-neg-in_binary64`
42×	`distribute-rgt-neg-out_binary64`
33×	`distribute-lft-neg-in_binary64` `associate--r+_binary64`
31×	`distribute-lft-neg-out_binary64`
25×	`*-commutative_binary64`
24×	`neg-sub0_binary64`
21×	`associate-+l-_binary64`
18×	`neg-mul-1_binary64`
15×	`distribute-neg-in_binary64` `+-commutative_binary64`
12×	`mul0-rgt_binary64` `mul0-lft_binary64`
9×	`sub0-neg_binary64`
6×	`associate--r-_binary64` `associate--l+_binary64` `associate-+r-_binary64` `associate-+r+_binary64`
3×	`*-lft-identity_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `distribute-rgt-out--_binary64` `associate-+l+_binary64`
1×	`1-exp_binary64` `swap-y-z`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow3_binary64` `unpow2_binary64` `unpow1/2_binary64` `pow-plus_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `exp-prod_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-unmult_binary64` `cube-mult_binary64` `cube-div_binary64` `cube-prod_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `times-frac_binary64` `div-sub_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `pow-sqr_binary64` `sqr-pow_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `unswap-sqr_binary64` `swap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-r/_binary64` `associate--l-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	41	40
2	105	40
3	198	40
4	213	40
5	378	40
6	341	40
7	482	40
8	473	40
9	476	40
10	476	40
11	423	40
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
18.7%	81.1%	0.1%	7
21.8%	78%	0.1%	8
43.7%	56.2%	0.1%	9
54.6%	39%	6.4%	10
58.5%	35.1%	6.4%	11
67.3%	26.3%	6.4%	12
71.7%	18.8%	9.5%	13
74.1%	16.4%	9.5%	14

Symmetry

(sort y z)

Compiler

Compiled 8 to 8 computations (0% saved)

sample25.0ms (1.1%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 15 to 18 computations (-20% saved)

simplify17.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

56×	`cancel-sign-sub-inv_binary64`
36×	`distribute-rgt-neg-in_binary64`
30×	`sub-neg_binary64`
20×	`distribute-lft-neg-in_binary64`
19×	`neg-mul-1_binary64` `distribute-rgt-in_binary64`
17×	`unsub-neg_binary64`
16×	`neg-sub0_binary64`
14×	`+-lft-identity_binary64` `associate-r_binary64`
13×	`distribute-lft-neg-out_binary64` `distribute-lft-in_binary64` `associate--r+_binary64` `*-commutative_binary64`
12×	`+-commutative_binary64`
10×	`distribute-rgt-neg-out_binary64` `associate-l_binary64`
9×	`sub0-neg_binary64` `associate-+l-_binary64`
8×	`mul0-rgt_binary64` `mul0-lft_binary64`
6×	`remove-double-neg_binary64` `--rgt-identity_binary64`
4×	`*-lft-identity_binary64` `distribute-neg-in_binary64`
3×	`associate-+l+_binary64`
2×	`*-rgt-identity_binary64` `associate--r-_binary64`
1×	`1-exp_binary64` `+-rgt-identity_binary64` `associate--l+_binary64` `associate-+r-_binary64` `associate-+r+_binary64`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow3_binary64` `unpow2_binary64` `unpow1/2_binary64` `pow-plus_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `exp-prod_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-unmult_binary64` `cube-mult_binary64` `cube-div_binary64` `cube-prod_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `times-frac_binary64` `div-sub_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `pow-sqr_binary64` `sqr-pow_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `unswap-sqr_binary64` `swap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64` `associate--l-_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	43	10
3	82	10
4	94	10
5	129	10
6	151	10
7	172	10
8	244	10
9	248	10
10	254	10
11	209	10

prune1.0ms (0.1%)

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

0.0b

Counts

1 → 1

Compiler

Compiled 7 to 7 computations (0% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(-.f64 x (.f64 (.f64 y 4) z))

rewrite15.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

3×	`add-log-exp_binary64`
1×	`diff-log_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `flip3--_binary64` `*-un-lft-identity_binary64` `sub-neg_binary64` `flip--_binary64` `cancel-sign-sub-inv_binary64`

Counts

1 → 12

Calls

1 calls:

3.0ms

(-.f64 x (*.f64 (*.f64 y 4) z))

Compiler

Compiled 187 to 123 computations (34.2% saved)

series35.0ms (1.6%)

Error

0.0b

Counts

1 → 18

Calls

1 calls:

32.0ms

(-.f64 x (*.f64 (*.f64 y 4) z))

Compiler

Compiled 168 to 177 computations (-5.4% saved)

simplify70.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

570×	`neg-mul-1_binary64`
462×	`unsub-neg_binary64`
368×	`associate-l_binary64`
357×	`distribute-rgt-neg-out_binary64`
330×	`cancel-sign-sub-inv_binary64`
296×	`distribute-rgt-in_binary64`
282×	`associate-r_binary64`
263×	`distribute-rgt-neg-in_binary64`
261×	`distribute-lft-neg-in_binary64`
246×	`distribute-lft-in_binary64`
213×	`neg-sub0_binary64`
119×	`distribute-neg-out_binary64`
114×	`sqr-pow_binary64`
90×	`distribute-neg-in_binary64`
88×	`distribute-lft-neg-out_binary64`
72×	`times-frac_binary64`
63×	`distribute-rgt-out_binary64`
60×	`exp-prod_binary64`
59×	`sub-neg_binary64`
56×	`*-commutative_binary64`
44×	`unswap-sqr_binary64`
41×	`mul0-rgt_binary64` `mul0-lft_binary64`
37×	`exp-sum_binary64`
35×	`swap-sqr_binary64`
28×	`associate-+r+_binary64`
25×	`distribute-lft-out_binary64`
24×	`pow-sqr_binary64`
23×	`difference-of-squares_binary64` `associate-+l+_binary64`
21×	`+-commutative_binary64`
20×	`cube-prod_binary64`
17×	`exp-diff_binary64`
13×	`div-sub_binary64`
12×	`unpow3_binary64` `cube-unmult_binary64`
8×	`cube-mult_binary64` `associate-/r*_binary64`
7×	`sqr-neg_binary64` `sub0-neg_binary64`
6×	`unpow2_binary64` `exp-neg_binary64` `mul-1-neg_binary64` `+-lft-identity_binary64` `associate-+l-_binary64`
5×	`+-rgt-identity_binary64` `distribute-frac-neg_binary64` `associate-+r-_binary64`
4×	`prod-exp_binary64` `associate-/l*_binary64`
3×	`unpow1_binary64`
2×	`pow-plus_binary64` `unpow-1_binary64` `cube-neg_binary64` `--rgt-identity_binary64` `associate--r+_binary64`
1×	`log-prod_binary64` `unpow1/2_binary64` `div-exp_binary64` `1-exp_binary64` `remove-double-neg_binary64` `cancel-sign-sub_binary64` `associate-/l/_binary64` `associate-*r/_binary64`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `rec-exp_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `distribute-neg-frac_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate-/r/_binary64` `associate-l/_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64`

Counts

30 → 19

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	348
1	104	324
2	320	324
3	1383	324
4	3052	324
5	4524	324
6	4897	324

prune8.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	17	2	19
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	17	3	20

Error

0.0b

Counts

20 → 3

Compiler

Compiled 162 to 99 computations (38.9% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 (.f64 -4 (.f64 z y)) x))
0.0b	(+.f64 (.f64 -4 (.f64 z y)) x)
0.0b	(+.f64 (.f64 -4 (.f64 z y)) x)
0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 -4 (.f64 z y)) x)) (sqrt.f64 (+.f64 (.f64 -4 (*.f64 z y)) x)))

rewrite114.0ms (5.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
20×	`pow1_binary64`
14×	`sqrt-div_binary64`
13×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64`
8×	`add-log-exp_binary64` `swap-sqr_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `associate-r_binary64`
5×	`pow-prod-up_binary64`
4×	`frac-times_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64`
2×	`associate-l/_binary64` `associate-r/_binary64` `sum-log_binary64` `+-commutative_binary64`
1×	`pow2_binary64` `pow-plus_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `sqrt-unprod_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64` `*-commutative_binary64`

Counts

4 → 95

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 -4 (.f64 z y)) x)) (sqrt.f64 (+.f64 (.f64 -4 (*.f64 z y)) x)))
8.0ms	(+.f64 (.f64 -4 (.f64 z y)) x)
5.0ms	(+.f64 (.f64 -4 (.f64 z y)) x)
5.0ms	(sqrt.f64 (+.f64 (.f64 -4 (.f64 z y)) x))

Compiler

Compiled 2306 to 1300 computations (43.6% saved)

series156.0ms (7%)

Error

0.0b

Counts

4 → 69

Calls

4 calls:

42.0ms	(sqrt.f64 (+.f64 (.f64 -4 (.f64 z y)) x))
35.0ms	(+.f64 (.f64 -4 (.f64 z y)) x)
35.0ms	(+.f64 (.f64 -4 (.f64 z y)) x)
33.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 -4 (.f64 z y)) x)) (sqrt.f64 (+.f64 (.f64 -4 (*.f64 z y)) x)))

Compiler

Compiled 1960 to 1537 computations (21.6% saved)

simplify142.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

474×	`cancel-sign-sub-inv_binary64`
395×	`unswap-sqr_binary64`
280×	`*-commutative_binary64`
244×	`unsub-neg_binary64`
154×	`neg-sub0_binary64`
149×	`exp-prod_binary64`
148×	`div-sub_binary64`
145×	`neg-mul-1_binary64`
132×	`cube-prod_binary64`
130×	`distribute-rgt-in_binary64`
121×	`times-frac_binary64`
119×	`sqr-pow_binary64`
116×	`distribute-lft-in_binary64` `associate-r_binary64`
115×	`associate-/r*_binary64`
107×	`associate-l_binary64`
106×	`distribute-rgt-neg-in_binary64`
96×	`sub-neg_binary64`
91×	`distribute-lft-neg-in_binary64`
61×	`distribute-rgt-neg-out_binary64`
60×	`associate-/l*_binary64`
58×	`swap-sqr_binary64`
51×	`distribute-lft-neg-out_binary64`
49×	`exp-sum_binary64`
42×	`log-prod_binary64`
34×	`+-commutative_binary64`
33×	`unpow3_binary64`
32×	`associate-+l+_binary64`
28×	`rem-sqrt-square_binary64` `remove-double-neg_binary64`
26×	`associate-*l/_binary64`
25×	`cube-mult_binary64` `associate-+r+_binary64`
22×	`exp-diff_binary64` `associate-*r/_binary64`
21×	`difference-of-squares_binary64`
20×	`distribute-rgt-out_binary64`
19×	`pow-sqr_binary64`
18×	`cube-neg_binary64` `mul0-rgt_binary64` `mul0-lft_binary64`
17×	`associate-+r-_binary64`
16×	`pow-plus_binary64` `associate-+l-_binary64`
15×	`sqr-neg_binary64` `distribute-lft-out_binary64`
14×	`*-rgt-identity_binary64`
13×	`*-lft-identity_binary64` `+-rgt-identity_binary64` `associate--l+_binary64`
11×	`cube-unmult_binary64` `distribute-neg-out_binary64`
10×	`distribute-neg-frac_binary64`
9×	`unpow2_binary64` `rem-square-sqrt_binary64` `sub0-neg_binary64` `distribute-rgt-out--_binary64`
8×	`log-pow_binary64`
7×	`associate-/r/_binary64`
6×	`unpow1/2_binary64`
5×	`distribute-lft-out--_binary64`
4×	`unpow1_binary64` `distribute-neg-in_binary64`
3×	`associate--l-_binary64`
2×	`prod-exp_binary64` `mul-1-neg_binary64` `--rgt-identity_binary64` `cancel-sign-sub_binary64` `count-2_binary64` `associate--r-_binary64` `associate--r+_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `/-rgt-identity_binary64` `+-lft-identity_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `distribute-frac-neg_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `associate-/l/_binary64`

Counts

164 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	2560
1	289	2423
2	941	2367
3	2723	2297
4	4647	2297
5	4894	2297

prune51.0ms (2.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	106	3	109

Error

0.0b

Counts

109 → 3

Compiler

Compiled 1364 to 779 computations (42.9% saved)

localize13.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 y (.f64 (*.f64 z y) 16))
2.6b	(-.f64 (.f64 z (.f64 y (.f64 (.f64 z y) 16))) (*.f64 x x))
4.7b	(.f64 z (.f64 y (.f64 (.f64 z y) 16)))
25.5b	(/.f64 (-.f64 (.f64 z (.f64 y (.f64 (.f64 z y) 16))) (.f64 x x)) (-.f64 (.f64 (*.f64 z y) -4) x))

rewrite115.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

29×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`pow1_binary64`
16×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
14×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
9×	`times-frac_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
3×	`flip3--_binary64` `flip--_binary64` `associate-/l_binary64` `associate-/r_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64` `associate-r_binary64` `*-commutative_binary64`
1×	`div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64` `diff-log_binary64` `sub-neg_binary64` `cancel-sign-sub-inv_binary64`

Counts

4 → 89

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (.f64 z (.f64 y (.f64 (.f64 z y) 16))) (.f64 x x)) (-.f64 (.f64 (*.f64 z y) -4) x))
10.0ms	(.f64 z (.f64 y (.f64 (.f64 z y) 16)))
9.0ms	(-.f64 (.f64 z (.f64 y (.f64 (.f64 z y) 16))) (*.f64 x x))
7.0ms	(.f64 y (.f64 (*.f64 z y) 16))

Compiler

Compiled 2749 to 1275 computations (53.6% saved)

series188.0ms (8.4%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

74.0ms	(/.f64 (-.f64 (.f64 z (.f64 y (.f64 (.f64 z y) 16))) (.f64 x x)) (-.f64 (.f64 (*.f64 z y) -4) x))
64.0ms	(-.f64 (.f64 z (.f64 y (.f64 (.f64 z y) 16))) (*.f64 x x))
23.0ms	(.f64 z (.f64 y (.f64 (.f64 z y) 16)))
20.0ms	(.f64 y (.f64 (*.f64 z y) 16))

Compiler

Compiled 1280 to 1077 computations (15.9% saved)

simplify129.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

570×	`associate-/l*_binary64`
440×	`times-frac_binary64`
264×	`associate-l_binary64`
241×	`associate-r_binary64`
175×	`distribute-rgt-in_binary64`
169×	`distribute-lft-in_binary64`
111×	`*-commutative_binary64`
98×	`div-sub_binary64`
95×	`cancel-sign-sub-inv_binary64` `associate-/l/_binary64`
89×	`swap-sqr_binary64`
79×	`distribute-rgt-neg-in_binary64`
73×	`unswap-sqr_binary64`
72×	`cube-prod_binary64` `distribute-lft-neg-in_binary64`
69×	`associate-/r/_binary64`
67×	`exp-prod_binary64`
54×	`log-div_binary64`
53×	`log-prod_binary64`
47×	`sqr-pow_binary64`
38×	`sub-neg_binary64`
37×	`distribute-lft-neg-out_binary64`
31×	`distribute-rgt-neg-out_binary64`
27×	`neg-mul-1_binary64` `neg-sub0_binary64`
26×	`+-commutative_binary64`
24×	`distribute-neg-frac_binary64`
19×	`distribute-rgt-out_binary64`
17×	`associate-+r+_binary64`
16×	`associate-/r*_binary64`
12×	`associate-*l/_binary64`
11×	`associate-+l+_binary64`
10×	`unpow3_binary64`
9×	`distribute-neg-in_binary64` `associate-*r/_binary64`
8×	`difference-of-squares_binary64`
7×	`cube-mult_binary64` `cube-div_binary64`
6×	`log-pow_binary64` `exp-sum_binary64` `/-rgt-identity_binary64` `*-rgt-identity_binary64` `pow-sqr_binary64`
5×	`exp-diff_binary64` `cube-unmult_binary64` `unsub-neg_binary64` `distribute-frac-neg_binary64` `distribute-lft-out_binary64`
4×	`pow-plus_binary64`
3×	`log-rec_binary64` `unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `rem-sqrt-square_binary64` `remove-double-neg_binary64` `associate-+r-_binary64`
2×	`+-rgt-identity_binary64` `*-inverses_binary64` `distribute-neg-out_binary64` `distribute-rgt-out--_binary64` `count-2_binary64` `associate--r-_binary64` `associate--r+_binary64`
1×	`div-exp_binary64` `1-exp_binary64` `cube-neg_binary64` `sqr-neg_binary64` `mul-1-neg_binary64` `*-lft-identity_binary64`
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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate-+l-_binary64`

Counts

137 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	3097
1	436	2854
2	1528	2773
3	4954	2773
4	4975	2773

prune47.0ms (2.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	111	3	114

Error

0.0b

Counts

114 → 3

Compiler

Compiled 1840 to 756 computations (58.9% saved)

regimes176.0ms (7.9%)

Accuracy

Total 0.0b remaining (44.9%)

Threshold costs 0.0b (44.9%)

Compiler

Compiled 1638 to 1434 computations (12.5% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`sub-neg_binary64` `+-commutative_binary64`
4×	`neg-mul-1_binary64` `neg-sub0_binary64` `distribute-rgt-neg-in_binary64`
3×	`distribute-lft-neg-in_binary64`
2×	`cancel-sign-sub-inv_binary64`
1×	`distribute-lft-neg-out_binary64`
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` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `unpow1_binary64` `e-exp-1_binary64` `1-exp_binary64` `exp-1-e_binary64` `exp-0_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `unsub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	15	10
2	32	10
3	40	10
4	46	10
5	48	10
6	47	10

end6.0ms (0.3%)

Remove: (sort y z)
Compiler: Compiled 21 to 21 computations (0% saved)

sample554.0ms (24.8%)

Algorithm

1×

intervals

Results

197.0ms	8000×	body	128	valid
7.0ms	305×	body	128	invalid

Compiler

Compiled 63 to 64 computations (-1.6% saved)

Iter	Nodes	Cost
0	16	40
1	41	40
2	105	40
3	198	40
4	213	40
5	378	40
6	341	40
7	482	40
8	473	40
9	476	40
10	476	40
11	423	40
0	3	3
1	3	3

Iter	Nodes	Cost
0	8	10
1	17	10
2	43	10
3	82	10
4	94	10
5	129	10
6	151	10
7	172	10
8	244	10
9	248	10
10	254	10
11	209	10

Iter	Nodes	Cost
0	16	40
1	41	40
2	105	40
3	198	40
4	213	40
5	378	40
6	341	40
7	482	40
8	473	40
9	476	40
10	476	40
11	423	40
0	3	3
1	3	3

Iter	Nodes	Cost
0	8	10
1	17	10
2	43	10
3	82	10
4	94	10
5	129	10
6	151	10
7	172	10
8	244	10
9	248	10
10	254	10
11	209	10

Details

analyze353.0ms (15.8%)

sample25.0ms (1.1%)

simplify17.0ms (0.8%)

prune1.0ms (0.1%)

localize5.0ms (0.2%)

rewrite15.0ms (0.7%)

series35.0ms (1.6%)

simplify70.0ms (3.1%)

prune8.0ms (0.4%)

localize8.0ms (0.4%)

rewrite114.0ms (5.1%)

series156.0ms (7%)

simplify142.0ms (6.4%)

prune51.0ms (2.3%)

localize13.0ms (0.6%)

rewrite115.0ms (5.2%)

series188.0ms (8.4%)

simplify129.0ms (5.8%)

prune47.0ms (2.1%)

regimes176.0ms (7.9%)

bsearch0.0ms (0%)

simplify4.0ms (0.2%)

end6.0ms (0.3%)

sample554.0ms (24.8%)

Profiling

Iter	Nodes	Cost
0	16	40
1	41	40
2	105	40
3	198	40
4	213	40
5	378	40
6	341	40
7	482	40
8	473	40
9	476	40
10	476	40
11	423	40
0	3	3
1	3	3

Iter	Nodes	Cost
0	8	10
1	17	10
2	43	10
3	82	10
4	94	10
5	129	10
6	151	10
7	172	10
8	244	10
9	248	10
10	254	10
11	209	10