Details

analyze31.0ms (1%)

Algorithm

1×	search
2×	egg-herbie

Rules

51×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
24×	`*-commutative_binary64`
21×	`associate-+r+_binary64` `+-commutative_binary64`
16×	`associate-+l+_binary64`
1×	`swap-a-b` `swap-a-c` `swap-a-d`
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` `1-exp_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` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-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` `mul0-rgt_binary64` `mul0-lft_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-inv_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` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_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` `associate-r*_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64` `swap-b-c` `swap-b-d` `swap-c-d`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	91
1	55	91
2	112	91
3	136	91
4	136	91
0	4	4
1	4	4

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Symmetry

(sort a b c d)

Compiler

Compiled 26 to 22 computations (15.4% saved)

sample41.0ms (1.3%)

Algorithm

1×

intervals

Results

10.0ms	256×	pre	128	true
7.0ms	256×	body	128	valid

Compiler

Compiled 35 to 35 computations (0% saved)

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

49×	`distribute-rgt-in_binary64`
46×	`distribute-lft-in_binary64`
40×	`associate-+l+_binary64`
32×	`associate-+r+_binary64`
17×	`+-commutative_binary64`
15×	`*-commutative_binary64`
3×	`distribute-rgt-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` `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` `1-exp_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` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-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` `mul0-rgt_binary64` `mul0-lft_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-inv_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` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_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` `associate-r*_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	52	13
3	118	13
4	157	13
5	149	13
6	136	13

prune1.0ms (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

3.8b

Counts

1 → 1

Compiler

Compiled 9 to 9 computations (0% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.4b	(+.f64 b (+.f64 c d))
3.0b	(+.f64 a (+.f64 b (+.f64 c d)))

rewrite44.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

1.2b

Rules

16×	`add-log-exp_binary64` `*-un-lft-identity_binary64`
9×	`sum-log_binary64` `distribute-lft-out_binary64`
2×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-+r+_binary64` `+-commutative_binary64`

Counts

2 → 32

Calls

2 calls:

15.0ms	(+.f64 a (+.f64 b (+.f64 c d)))
6.0ms	(+.f64 b (+.f64 c d))

Compiler

Compiled 438 to 155 computations (64.6% saved)

series60.0ms (2%)

Error

3.0b

Counts

2 → 42

Calls

2 calls:

31.0ms	(+.f64 a (+.f64 b (+.f64 c d)))
21.0ms	(+.f64 b (+.f64 c d))

Compiler

Compiled 568 to 572 computations (-0.7% saved)

simplify79.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

791×	`associate--l+_binary64`
706×	`distribute-rgt-in_binary64`
651×	`distribute-lft-in_binary64`
390×	`associate-l_binary64`
248×	`associate-+r+_binary64`
245×	`associate-+l+_binary64`
220×	`distribute-neg-in_binary64`
214×	`associate-r_binary64`
203×	`sub-neg_binary64`
150×	`unsub-neg_binary64`
136×	`neg-sub0_binary64`
135×	`cancel-sign-sub-inv_binary64`
115×	`distribute-rgt-out_binary64` `associate--r+_binary64`
111×	`neg-mul-1_binary64`
85×	`*-commutative_binary64`
68×	`distribute-lft-neg-out_binary64`
63×	`distribute-rgt-neg-out_binary64`
61×	`associate--l-_binary64`
56×	`+-commutative_binary64`
30×	`distribute-rgt-out--_binary64`
19×	`exp-sum_binary64`
18×	`sqr-pow_binary64` `associate-+r-_binary64`
16×	`prod-exp_binary64` `associate-+l-_binary64`
15×	`+-rgt-identity_binary64` `distribute-rgt-neg-in_binary64`
12×	`distribute-lft-neg-in_binary64` `associate--r-_binary64`
9×	`cube-unmult_binary64`
8×	`sub0-neg_binary64` `unswap-sqr_binary64`
6×	`difference-of-squares_binary64`
4×	`unpow3_binary64` `pow-plus_binary64` `cube-mult_binary64`
1×	`1-exp_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` `unpow2_binary64` `unpow1/2_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` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_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` `-lft-identity_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `pow-sqr_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_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-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`

Counts

74 → 40

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	63	666
1	188	645
2	650	645
3	3157	645
4	4887	645
5	4960	645

prune24.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	33	7	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	7	41

Error

2.3b

Counts

41 → 7

Compiler

Compiled 456 to 207 computations (54.6% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

3.0b	(+.f64 d (+.f64 (+.f64 b c) a))

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.9b

Rules

10×	`add-log-exp_binary64` `*-un-lft-identity_binary64`
6×	`sum-log_binary64` `distribute-lft-out_binary64`
1×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `flip3-+_binary64` `flip-+_binary64` `associate-+r+_binary64` `+-commutative_binary64`

Counts

1 → 17

Calls

1 calls:

8.0ms

(+.f64 d (+.f64 (+.f64 b c) a))

Compiler

Compiled 236 to 83 computations (64.8% saved)

series33.0ms (1.1%)

Error

2.3b

Counts

1 → 24

Calls

1 calls:

29.0ms

(+.f64 d (+.f64 (+.f64 b c) a))

Compiler

Compiled 317 to 326 computations (-2.8% saved)

simplify64.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

638×	`distribute-rgt-in_binary64`
608×	`distribute-lft-in_binary64`
456×	`associate--l+_binary64`
444×	`distribute-neg-in_binary64`
431×	`associate--r+_binary64`
391×	`associate-l_binary64`
215×	`associate-r_binary64`
204×	`unsub-neg_binary64`
183×	`associate-+r+_binary64`
162×	`associate-+l+_binary64`
128×	`associate-+l-_binary64`
122×	`sub-neg_binary64`
110×	`neg-sub0_binary64`
93×	`cancel-sign-sub-inv_binary64`
83×	`distribute-rgt-out_binary64`
76×	`neg-mul-1_binary64` `*-commutative_binary64`
72×	`distribute-lft-neg-out_binary64`
69×	`distribute-rgt-neg-out_binary64`
51×	`sub0-neg_binary64`
41×	`associate--l-_binary64`
35×	`+-commutative_binary64`
28×	`cancel-sign-sub_binary64`
24×	`unswap-sqr_binary64`
19×	`prod-exp_binary64`
18×	`distribute-rgt-out--_binary64`
15×	`exp-sum_binary64` `sqr-pow_binary64`
9×	`difference-of-squares_binary64` `distribute-rgt-neg-in_binary64`
7×	`distribute-lft-neg-in_binary64` `associate--r-_binary64` `associate-+r-_binary64`
6×	`mul-1-neg_binary64` `+-rgt-identity_binary64`
5×	`cube-unmult_binary64`
3×	`--rgt-identity_binary64`
2×	`unpow3_binary64` `pow-plus_binary64` `cube-mult_binary64` `remove-double-neg_binary64` `distribute-neg-out_binary64` `distribute-lft-out_binary64`
1×	`1-exp_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` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `unpow1/2_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` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_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` `/-rgt-identity_binary64` `-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `pow-sqr_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `swap-sqr_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_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`

Counts

41 → 27

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	422
1	121	401
2	483	401
3	2631	401
4	4567	401
5	5023	401

prune13.0ms (0.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	25	9	34

Error

2.0b

Counts

34 → 9

Compiler

Compiled 355 to 167 computations (53% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.6b	(cbrt.f64 (pow.f64 (+.f64 d (+.f64 (+.f64 b c) a)) 3))
3.0b	(+.f64 d (+.f64 (+.f64 b c) a))

rewrite53.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.9b

Rules

32×	`*-un-lft-identity_binary64`
18×	`distribute-lft-out_binary64` `cbrt-prod_binary64`
11×	`add-log-exp_binary64`
6×	`sum-log_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
5×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip3-+_binary64` `flip-+_binary64` `cube-div_binary64` `cbrt-div_binary64`
1×	`associate-+r+_binary64` `+-commutative_binary64` `pow1/3_binary64` `unpow3_binary64` `cube-mult_binary64` `sqr-pow_binary64` `rem-cbrt-cube_binary64`

Counts

2 → 46

Calls

2 calls:

9.0ms	(cbrt.f64 (pow.f64 (+.f64 d (+.f64 (+.f64 b c) a)) 3))
8.0ms	(+.f64 d (+.f64 (+.f64 b c) a))

Compiler

Compiled 760 to 307 computations (59.6% saved)

series74.0ms (2.4%)

Error

2.0b

Counts

2 → 48

Calls

2 calls:

36.0ms	(+.f64 d (+.f64 (+.f64 b c) a))
30.0ms	(cbrt.f64 (pow.f64 (+.f64 d (+.f64 (+.f64 b c) a)) 3))

Compiler

Compiled 769 to 775 computations (-0.8% saved)

simplify53.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

927×	`distribute-rgt-in_binary64`
894×	`distribute-lft-in_binary64`
463×	`associate-l_binary64`
371×	`associate-r_binary64`
51×	`unswap-sqr_binary64`
50×	`distribute-neg-in_binary64`
35×	`sqr-pow_binary64`
32×	`sub-neg_binary64`
20×	`+-commutative_binary64`
19×	`distribute-lft-neg-out_binary64` `*-commutative_binary64`
18×	`cancel-sign-sub-inv_binary64`
17×	`distribute-rgt-neg-out_binary64` `associate-+l+_binary64`
14×	`neg-mul-1_binary64` `neg-sub0_binary64` `distribute-rgt-out_binary64` `associate-+r+_binary64`
12×	`prod-exp_binary64` `distribute-lft-out_binary64` `associate--r+_binary64`
11×	`unpow3_binary64` `exp-sum_binary64`
10×	`cube-mult_binary64`
9×	`cube-prod_binary64`
8×	`rem-cbrt-cube_binary64`
7×	`unsub-neg_binary64` `distribute-rgt-neg-in_binary64`
6×	`log-prod_binary64` `exp-prod_binary64` `rem-sqrt-square_binary64` `associate--l+_binary64`
5×	`swap-sqr_binary64` `distribute-lft-neg-in_binary64`
3×	`pow-plus_binary64` `distribute-rgt-out--_binary64`
2×	`log-pow_binary64` `cube-unmult_binary64` `pow-sqr_binary64`
1×	`1-exp_binary64` `rem-3cbrt-lft_binary64` `rem-cube-cbrt_binary64` `rem-square-sqrt_binary64` `difference-of-squares_binary64` `count-2_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-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `unpow1/2_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` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `times-frac_binary64` `div-sub_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` `mul0-rgt_binary64` `mul0-lft_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` `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-lft-out--_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

94 → 65

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	80	1134
1	184	1085
2	743	1085
3	5014	1085

prune32.0ms (1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	55	10	65
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	59	15	74

Error

1.9b

Counts

74 → 15

Compiler

Compiled 749 to 370 computations (50.6% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.6b	(cbrt.f64 (pow.f64 (+.f64 (+.f64 (+.f64 b c) d) a) 3))
3.0b	(+.f64 (+.f64 (+.f64 b c) d) a)

rewrite60.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

32×	`*-un-lft-identity_binary64`
18×	`distribute-lft-out_binary64` `cbrt-prod_binary64`
11×	`add-log-exp_binary64`
6×	`sum-log_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
5×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip3-+_binary64` `flip-+_binary64` `cube-div_binary64` `cbrt-div_binary64`
1×	`associate-+l+_binary64` `+-commutative_binary64` `pow1/3_binary64` `unpow3_binary64` `cube-mult_binary64` `sqr-pow_binary64` `rem-cbrt-cube_binary64`

Counts

2 → 46

Calls

2 calls:

10.0ms	(cbrt.f64 (pow.f64 (+.f64 (+.f64 (+.f64 b c) d) a) 3))
9.0ms	(+.f64 (+.f64 (+.f64 b c) d) a)

Compiler

Compiled 760 to 307 computations (59.6% saved)

series75.0ms (2.4%)

Error

1.9b

Counts

2 → 48

Calls

2 calls:

35.0ms	(+.f64 (+.f64 (+.f64 b c) d) a)
31.0ms	(cbrt.f64 (pow.f64 (+.f64 (+.f64 (+.f64 b c) d) a) 3))

Compiler

Compiled 769 to 775 computations (-0.8% saved)

simplify74.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

545×	`distribute-rgt-out_binary64`
446×	`associate-l_binary64`
427×	`distribute-lft-out_binary64`
375×	`unswap-sqr_binary64`
355×	`associate-r_binary64`
226×	`associate-+l+_binary64`
145×	`*-commutative_binary64`
142×	`associate-+r+_binary64`
86×	`sub-neg_binary64`
77×	`cancel-sign-sub-inv_binary64`
71×	`+-commutative_binary64`
66×	`distribute-neg-in_binary64` `distribute-rgt-in_binary64`
62×	`distribute-lft-in_binary64`
60×	`sqr-pow_binary64`
46×	`associate--r+_binary64`
44×	`unsub-neg_binary64`
35×	`associate--l+_binary64`
28×	`distribute-lft-neg-in_binary64`
27×	`neg-sub0_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64`
26×	`cube-prod_binary64`
24×	`distribute-rgt-neg-out_binary64`
22×	`neg-mul-1_binary64`
17×	`swap-sqr_binary64`
16×	`prod-exp_binary64`
15×	`unpow3_binary64`
14×	`exp-sum_binary64`
13×	`cube-unmult_binary64` `cube-mult_binary64` `associate-+r-_binary64`
11×	`distribute-rgt-out--_binary64`
10×	`pow-plus_binary64` `+-rgt-identity_binary64`
9×	`log-prod_binary64` `exp-prod_binary64` `rem-sqrt-square_binary64`
8×	`rem-cbrt-cube_binary64`
7×	`pow-sqr_binary64` `associate-+l-_binary64`
3×	`log-pow_binary64` `sub0-neg_binary64` `difference-of-squares_binary64`
1×	`1-exp_binary64` `rem-3cbrt-lft_binary64` `rem-cube-cbrt_binary64` `rem-square-sqrt_binary64` `count-2_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` `unpow2_binary64` `unpow1/2_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` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `times-frac_binary64` `div-sub_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_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` `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-lft-out--_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

94 → 66

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	81	1143
1	182	1094
2	699	1082
3	2523	1082
4	5092	1082

prune18.0ms (0.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	66	15	81

Error

1.9b

Counts

81 → 15

Compiler

Compiled 422 to 151 computations (64.2% saved)

regimes965.0ms (31.4%)

Accuracy

Total -1.1b remaining (-190.1%)

Threshold costs -1.1b (-190.1%)

Compiler

Compiled 12214 to 9414 computations (22.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`*-commutative_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` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-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-inv_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` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	17	18
2	17	18

end13.0ms (0.4%)

Remove: (sort a b c d)
Compiler: Compiled 36 to 36 computations (0% saved)

sample1.2s (39%)

Algorithm

1×

intervals

Results

305.0ms	8000×	pre	128	true
220.0ms	8000×	body	128	valid

Compiler

Compiled 421 to 303 computations (28% saved)

Details

analyze31.0ms (1%)

sample41.0ms (1.3%)

simplify12.0ms (0.4%)

prune1.0ms (0%)

localize6.0ms (0.2%)

rewrite44.0ms (1.4%)

series60.0ms (2%)

simplify79.0ms (2.6%)

prune24.0ms (0.8%)

localize6.0ms (0.2%)

rewrite23.0ms (0.7%)

series33.0ms (1.1%)

simplify64.0ms (2.1%)

prune13.0ms (0.4%)

localize9.0ms (0.3%)

rewrite53.0ms (1.7%)

series74.0ms (2.4%)

simplify53.0ms (1.7%)

prune32.0ms (1%)

localize9.0ms (0.3%)

rewrite60.0ms (2%)

series75.0ms (2.4%)

simplify74.0ms (2.4%)

prune18.0ms (0.6%)

regimes965.0ms (31.4%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end13.0ms (0.4%)

sample1.2s (39%)

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