Details

analyze2.1s (2.7%)

Algorithm

1×

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
31.2%	68.7%	0.1%	7
34.3%	65.6%	0.1%	8
37.5%	59.3%	3.2%	9
42.9%	53.5%	3.6%	10
44.5%	50%	5.6%	11
47.8%	45.8%	6.4%	12
48.7%	43.7%	7.6%	13
50.5%	41.3%	8.2%	14

Compiler

Compiled 128 to 81 computations (36.7% saved)

sample145.0ms (0.2%)

Algorithm

1×

intervals

Results

52.0ms	222×	body	128	valid
43.0ms	197×	body	128	invalid
11.0ms	12×	body	1024	valid
9.0ms	13×	body	512	valid
4.0ms	9×	body	256	valid

Compiler

Compiled 255 to 163 computations (36.1% saved)

simplify246.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

814×	`distribute-rgt-in_binary64`
785×	`distribute-lft-in_binary64`
161×	`associate-+l+_binary64`
160×	`distribute-lft-out_binary64`
148×	`associate-l_binary64`
146×	`associate-r_binary64`
135×	`associate-+r+_binary64`
126×	`distribute-rgt-out_binary64`
68×	`*-commutative_binary64`
59×	`distribute-lft-neg-out_binary64`
56×	`distribute-rgt-neg-out_binary64`
49×	`sub-neg_binary64` `+-commutative_binary64`
43×	`div-sub_binary64`
35×	`associate-*r/_binary64`
34×	`unsub-neg_binary64`
33×	`associate-*l/_binary64`
30×	`neg-sub0_binary64`
29×	`associate-/l*_binary64`
23×	`*-rgt-identity_binary64`
22×	`neg-mul-1_binary64`
21×	`*-lft-identity_binary64`
18×	`cancel-sign-sub-inv_binary64`
10×	`associate-+l-_binary64` `associate-+r-_binary64`
9×	`distribute-rgt-neg-in_binary64`
7×	`+-rgt-identity_binary64` `distribute-lft-neg-in_binary64`
6×	`swap-sqr_binary64` `distribute-neg-frac_binary64` `distribute-neg-in_binary64`
5×	`sub0-neg_binary64` `associate--l+_binary64`
4×	`distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `associate-/r/_binary64`
3×	`associate--l-_binary64`
2×	`remove-double-neg_binary64` `--rgt-identity_binary64` `sqr-pow_binary64` `distribute-neg-out_binary64` `associate--r-_binary64`
1×	`prod-exp_binary64` `1-exp_binary64` `cube-unmult_binary64` `pow-sqr_binary64` `count-2_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` `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-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` `mul-1-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` `difference-of-squares_binary64` `unswap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `associate-/l/_binary64` `associate-/r_binary64`

Counts

1 → 4

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	190
1	109	187
2	362	178
3	1666	157

prune49.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	1	3	4
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	3	5

Error

0.5b

Counts

5 → 3

Compiler

Compiled 833 to 522 computations (37.3% saved)

localize45.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (.f64 x1 2) (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3))
2.8b	(+.f64 (.f64 (.f64 (.f64 x1 2) (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 x1 (.f64 x1 (-.f64 (/.f64 (.f64 4 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1)) (+.f64 (.f64 x1 x1) 1)) 6))))
3.3b	(-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)
5.7b	(.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1))

rewrite1.7s (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

37×	`associate-*r/_binary64`
33×	`cancel-sign-sub-inv_binary64`
31×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
29×	`add-sqr-sqrt_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64`
23×	`*-un-lft-identity_binary64`
22×	`pow1_binary64`
17×	`prod-exp_binary64` `add-cube-cbrt_binary64` `cbrt-unprod_binary64`
16×	`associate-+r+_binary64`
13×	`flip3--_binary64` `flip--_binary64`
12×	`pow-prod-down_binary64`
11×	`sub-neg_binary64` `associate-r_binary64`
10×	`frac-add_binary64`
8×	`add-log-exp_binary64` `associate-+l+_binary64`
6×	`frac-times_binary64`
5×	`difference-of-squares_binary64`
3×	`distribute-lft-out--_binary64` `associate-*l/_binary64`
2×	`associate--l+_binary64` `associate-l_binary64` `*-commutative_binary64` `times-frac_binary64` `div-exp_binary64` `cbrt-undiv_binary64`
1×	`diff-log_binary64` `div-sub_binary64` `associate--l-_binary64` `sum-log_binary64` `flip3-+_binary64` `flip-+_binary64` `+-commutative_binary64`

Counts

4 → 139

Calls

4 calls:

45.0ms	(+.f64 (.f64 (.f64 (.f64 x1 2) (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 x1 (.f64 x1 (-.f64 (/.f64 (.f64 4 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1)) (+.f64 (.f64 x1 x1) 1)) 6))))
37.0ms	(.f64 (.f64 (.f64 x1 2) (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3))
23.0ms	(-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)
18.0ms	(.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1))

Compiler

Compiled 22441 to 13934 computations (37.9% saved)

series4.2s (5.3%)

Error

0.4b

Counts

4 → 66

Calls

4 calls:

2.5s	(+.f64 (.f64 (.f64 (.f64 x1 2) (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 x1 (.f64 x1 (-.f64 (/.f64 (.f64 4 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1)) (+.f64 (.f64 x1 x1) 1)) 6))))
500.0ms	(-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)
452.0ms	(.f64 (.f64 (.f64 x1 2) (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3))
294.0ms	(.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1))

Compiler

Compiled 18195 to 12154 computations (33.2% saved)

simplify1.6s (2%)

Algorithm

1×	egg-herbie

Rules

327×	`distribute-rgt-in_binary64`
318×	`distribute-lft-in_binary64`
179×	`*-commutative_binary64`
168×	`associate--r+_binary64`
155×	`associate--l+_binary64`
144×	`associate-*l/_binary64`
139×	`associate-*r/_binary64`
130×	`sub-neg_binary64`
126×	`+-commutative_binary64`
124×	`associate-/l*_binary64`
92×	`times-frac_binary64` `associate-l_binary64`
88×	`cancel-sign-sub-inv_binary64`
76×	`associate-r_binary64`
72×	`associate-/r*_binary64`
60×	`associate-+r+_binary64`
59×	`distribute-neg-in_binary64`
54×	`neg-mul-1_binary64` `neg-sub0_binary64`
42×	`distribute-rgt-neg-in_binary64`
36×	`sqr-pow_binary64`
28×	`swap-sqr_binary64`
27×	`distribute-lft-neg-in_binary64`
26×	`unswap-sqr_binary64`
25×	`distribute-lft-neg-out_binary64`
21×	`exp-prod_binary64`
17×	`log-prod_binary64`
14×	`unpow3_binary64` `cube-prod_binary64` `pow-sqr_binary64`
13×	`distribute-rgt-neg-out_binary64`
12×	`*-rgt-identity_binary64`
11×	`distribute-rgt-out_binary64`
10×	`cube-mult_binary64` `associate-/r/_binary64`
8×	`difference-of-squares_binary64`
6×	`cube-unmult_binary64`
4×	`unpow2_binary64` `cube-div_binary64` `*-lft-identity_binary64`
3×	`div-sub_binary64` `associate-+l+_binary64`
2×	`log-div_binary64` `pow-plus_binary64` `rem-3cbrt-lft_binary64` `rem-square-sqrt_binary64` `unsub-neg_binary64` `distribute-rgt-out--_binary64` `associate-+r-_binary64`
1×	`exp-lft-cube_binary64` `div-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-sum_binary64` `1-exp_binary64` `*-inverses_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate--l-_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` `pow-base-0_binary64` `unpow1/3_binary64` `unpow1/2_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `mul-1-neg_binary64` `/-rgt-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` `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`

Counts

205 → 550

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	553	15695
1	1780	14830

prune10.9s (13.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	541	9	550
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	543	10	553

Error

0.4b

Counts

553 → 10

Compiler

Compiled 96225 to 59758 computations (37.9% saved)

localize48.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3) (.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (.f64 x1 2)))
2.8b	(+.f64 (/.f64 (.f64 (-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3) (.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (.f64 x1 2))) (+.f64 (.f64 x1 x1) 1)) (.f64 x1 (.f64 x1 (-.f64 (/.f64 (.f64 4 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1)) (+.f64 (.f64 x1 x1) 1)) 6))))
3.3b	(-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)
5.7b	(.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1))

rewrite1.2s (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

25×	`add-sqr-sqrt_binary64`
22×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
21×	`distribute-rgt-in_binary64` `cancel-sign-sub-inv_binary64` `distribute-lft-in_binary64`
19×	`*-un-lft-identity_binary64`
16×	`associate-+r+_binary64`
13×	`add-cube-cbrt_binary64`
12×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`add-log-exp_binary64` `associate-r/_binary64` `associate-l/_binary64`
7×	`sub-neg_binary64` `associate-l_binary64`
6×	`associate-r_binary64`
5×	`difference-of-squares_binary64`
4×	`frac-times_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate--l+_binary64` `*-commutative_binary64` `times-frac_binary64` `frac-add_binary64`
1×	`diff-log_binary64` `div-sub_binary64` `associate--l-_binary64` `sum-log_binary64` `flip3-+_binary64` `flip-+_binary64` `+-commutative_binary64`

Counts

4 → 114

Calls

4 calls:

44.0ms	(+.f64 (/.f64 (.f64 (-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3) (.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (.f64 x1 2))) (+.f64 (.f64 x1 x1) 1)) (.f64 x1 (.f64 x1 (-.f64 (/.f64 (.f64 4 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1)) (+.f64 (.f64 x1 x1) 1)) 6))))
39.0ms	(.f64 (-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3) (.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (.f64 x1 2)))
19.0ms	(-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)
16.0ms	(.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1))

Compiler

Compiled 17327 to 10709 computations (38.2% saved)

series4.0s (5.1%)

Error

0.4b

Counts

4 → 66

Calls

4 calls:

2.5s	(+.f64 (/.f64 (.f64 (-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3) (.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (.f64 x1 2))) (+.f64 (.f64 x1 x1) 1)) (.f64 x1 (.f64 x1 (-.f64 (/.f64 (.f64 4 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1)) (+.f64 (.f64 x1 x1) 1)) 6))))
476.0ms	(-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3)
366.0ms	(.f64 (-.f64 (/.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (+.f64 (.f64 x1 x1) 1)) 3) (.f64 (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1) (.f64 x1 2)))
287.0ms	(.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (.f64 2 x2)) x1))

Compiler

Compiled 18253 to 12118 computations (33.6% saved)

simplify1.2s (1.5%)

Algorithm

1×	egg-herbie

Rules

633×	`associate-l_binary64`
612×	`associate-r_binary64`
216×	`distribute-rgt-in_binary64`
210×	`distribute-lft-in_binary64`
152×	`*-commutative_binary64`
131×	`sub-neg_binary64`
124×	`+-commutative_binary64`
117×	`associate-/l*_binary64`
83×	`cancel-sign-sub-inv_binary64`
73×	`associate-*r/_binary64`
71×	`associate-+r+_binary64`
62×	`distribute-neg-in_binary64`
61×	`times-frac_binary64`
60×	`associate-*l/_binary64`
51×	`neg-mul-1_binary64` `neg-sub0_binary64`
46×	`associate-/r*_binary64`
35×	`sqr-pow_binary64` `distribute-rgt-neg-in_binary64`
28×	`associate--r+_binary64`
26×	`swap-sqr_binary64` `associate--l+_binary64`
22×	`distribute-lft-neg-in_binary64`
19×	`distribute-lft-neg-out_binary64`
18×	`unswap-sqr_binary64`
15×	`exp-prod_binary64`
14×	`log-prod_binary64` `pow-sqr_binary64`
13×	`unpow3_binary64` `distribute-rgt-out_binary64`
11×	`cube-mult_binary64`
10×	`associate-/r/_binary64`
9×	`cube-prod_binary64`
8×	`cube-unmult_binary64` `difference-of-squares_binary64` `distribute-rgt-neg-out_binary64`
6×	`*-rgt-identity_binary64`
5×	`cube-div_binary64`
4×	`unpow2_binary64`
3×	`distribute-neg-frac_binary64`
2×	`rem-3cbrt-lft_binary64` `rem-square-sqrt_binary64` `div-sub_binary64` `*-lft-identity_binary64` `distribute-rgt-out--_binary64` `associate-+l+_binary64`
1×	`pow-plus_binary64` `exp-lft-cube_binary64` `div-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-sum_binary64` `1-exp_binary64` `*-inverses_binary64` `distribute-rgt1-in_binary64` `distribute-lft-out_binary64` `count-2_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` `unpow1/2_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `unsub-neg_binary64` `mul-1-neg_binary64` `/-rgt-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` `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-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `associate-/l/_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate-+l-_binary64`

Counts

180 → 394

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	514	11523
1	1526	10554

prune6.3s (7.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	392	2	394
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	394	10	404

Error

0.4b

Counts

404 → 10

Compiler

Compiled 63864 to 39351 computations (38.4% saved)

localize38.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) 4)))
2.8b	(-.f64 (.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) 6))
3.3b	(-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)
5.7b	(.f64 (.f64 x1 x1) (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)))

rewrite1.0s (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

33×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `times-frac_binary64`
20×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`
16×	`associate-l_binary64`
11×	`pow1_binary64`
8×	`prod-exp_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64`
4×	`pow-prod-down_binary64` `unswap-sqr_binary64` `flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64` `cancel-sign-sub-inv_binary64`
3×	`div-exp_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64`
2×	`div-inv_binary64` `*-commutative_binary64` `diff-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `difference-of-squares_binary64` `distribute-rgt-in_binary64` `associate--l+_binary64` `distribute-lft-in_binary64` `frac-times_binary64`
1×	`distribute-lft-out--_binary64` `associate-+r-_binary64` `div-sub_binary64` `associate--l-_binary64` `associate-*l/_binary64`

Counts

4 → 109

Calls

4 calls:

42.0ms	(.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) 4)))
40.0ms	(-.f64 (.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) 6))
23.0ms	(-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)
20.0ms	(.f64 (.f64 x1 x1) (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)))

Compiler

Compiled 14312 to 8327 computations (41.8% saved)

series5.2s (6.6%)

Error

0.4b

Counts

4 → 77

Calls

4 calls:

2.5s	(-.f64 (.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 (.f64 x1 x1) 6))
1.4s	(.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) 4)))
465.0ms	(-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)
322.0ms	(.f64 (.f64 x1 x1) (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)))

Compiler

Compiled 18958 to 12868 computations (32.1% saved)

simplify1.5s (1.8%)

Algorithm

1×	egg-herbie

Rules

517×	`associate-l_binary64`
495×	`associate-r_binary64`
202×	`associate-/l*_binary64`
177×	`sub-neg_binary64`
172×	`associate-*r/_binary64`
171×	`distribute-rgt-in_binary64`
163×	`distribute-lft-in_binary64`
159×	`associate-*l/_binary64`
140×	`+-commutative_binary64`
135×	`*-commutative_binary64`
125×	`cancel-sign-sub-inv_binary64`
113×	`times-frac_binary64`
84×	`associate-+r+_binary64`
76×	`associate-/r*_binary64`
58×	`distribute-neg-in_binary64`
51×	`unswap-sqr_binary64`
46×	`neg-mul-1_binary64` `neg-sub0_binary64`
45×	`distribute-rgt-neg-in_binary64`
39×	`sqr-pow_binary64`
36×	`associate--r+_binary64`
35×	`associate--l+_binary64`
32×	`distribute-lft-neg-in_binary64`
26×	`associate-/l/_binary64`
20×	`associate-/r/_binary64`
18×	`swap-sqr_binary64`
17×	`cube-prod_binary64` `pow-sqr_binary64`
16×	`unpow3_binary64` `distribute-rgt-out_binary64`
15×	`exp-prod_binary64`
12×	`cube-mult_binary64` `distribute-lft-neg-out_binary64`
11×	`*-rgt-identity_binary64`
10×	`log-prod_binary64`
8×	`difference-of-squares_binary64`
7×	`div-sub_binary64`
5×	`log-div_binary64` `distribute-lft-out_binary64` `count-2_binary64`
4×	`unpow2_binary64` `pow-plus_binary64` `cube-div_binary64` `*-lft-identity_binary64` `distribute-rgt-out--_binary64` `associate-+r-_binary64`
3×	`div-exp_binary64` `exp-sum_binary64` `/-rgt-identity_binary64` `distribute-neg-frac_binary64`
2×	`pow-base-1_binary64` `cube-unmult_binary64` `difference-of-sqr-1_binary64` `distribute-lft-out--_binary64`
1×	`rec-exp_binary64` `prod-exp_binary64` `1-exp_binary64` `rem-3cbrt-lft_binary64` `rem-square-sqrt_binary64` `*-inverses_binary64` `distribute-rgt-neg-out_binary64` `distribute-rgt1-in_binary64` `associate-+l-_binary64` `associate-+l+_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` `pow-base-0_binary64` `unpow1/3_binary64` `unpow1/2_binary64` `exp-to-pow_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_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-neg_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `unsub-neg_binary64` `mul-1-neg_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` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

186 → 393

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	534	11645
1	1651	10892

prune4.7s (6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	390	3	393
Fresh	2	6	8
Picked	1	0	1
Done	1	0	1
Total	394	9	403

Error

0.4b

Counts

403 → 9

Compiler

Compiled 53732 to 31353 computations (41.6% saved)

localize37.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) 4)))
2.8b	(+.f64 (.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 x1 (.f64 (neg.f64 x1) 6)))
3.3b	(-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)
5.7b	(.f64 (.f64 x1 x1) (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)))

rewrite1.0s (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

33×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `times-frac_binary64`
20×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`
16×	`associate-l_binary64`
11×	`pow1_binary64`
8×	`prod-exp_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`pow-prod-down_binary64` `unswap-sqr_binary64` `associate-/r/_binary64`
3×	`div-exp_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `cancel-sign-sub-inv_binary64`
2×	`div-inv_binary64` `*-commutative_binary64` `difference-of-squares_binary64` `distribute-rgt-in_binary64` `associate-+l+_binary64` `distribute-lft-in_binary64` `frac-times_binary64`
1×	`diff-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `distribute-lft-out--_binary64` `associate-+r-_binary64` `div-sub_binary64` `associate--l-_binary64` `sum-log_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-out_binary64` `unsub-neg_binary64` `+-commutative_binary64` `associate-*l/_binary64`

Counts

4 → 109

Calls

4 calls:

44.0ms	(+.f64 (.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 x1 (.f64 (neg.f64 x1) 6)))
40.0ms	(.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) 4)))
19.0ms	(.f64 (.f64 x1 x1) (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)))
19.0ms	(-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)

Compiler

Compiled 14428 to 8445 computations (41.5% saved)

series5.3s (6.6%)

Error

0.4b

Counts

4 → 77

Calls

4 calls:

2.5s	(+.f64 (.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) 4))) (.f64 x1 (.f64 (neg.f64 x1) 6)))
1.5s	(.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) (+.f64 (.f64 (+.f64 x1 x1) (-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)) (.f64 (.f64 x1 x1) 4)))
487.0ms	(-.f64 (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)) 3)
341.0ms	(.f64 (.f64 x1 x1) (/.f64 (+.f64 (.f64 x1 (.f64 x1 3)) (-.f64 (.f64 2 x2) x1)) (+.f64 (.f64 x1 x1) 1)))

Compiler

Compiled 19079 to 13055 computations (31.6% saved)

simplify1.5s (1.9%)

Algorithm

1×	egg-herbie

Rules

522×	`associate-l_binary64`
509×	`associate-r_binary64`
201×	`associate-/l*_binary64`
185×	`distribute-rgt-in_binary64`
176×	`sub-neg_binary64`
174×	`associate-*r/_binary64`
173×	`distribute-lft-in_binary64`
160×	`associate-*l/_binary64`
141×	`+-commutative_binary64`
137×	`*-commutative_binary64`
125×	`cancel-sign-sub-inv_binary64`
112×	`times-frac_binary64`
83×	`associate-+r+_binary64`
76×	`associate-/r*_binary64`
59×	`distribute-neg-in_binary64`
52×	`unswap-sqr_binary64`
48×	`distribute-rgt-neg-in_binary64`
47×	`neg-mul-1_binary64` `neg-sub0_binary64`
39×	`sqr-pow_binary64`
36×	`associate--r+_binary64`
35×	`associate--l+_binary64`
34×	`distribute-lft-neg-in_binary64`
26×	`associate-/l/_binary64`
20×	`swap-sqr_binary64` `associate-/r/_binary64`
19×	`cube-prod_binary64`
17×	`pow-sqr_binary64` `distribute-lft-neg-out_binary64`
16×	`unpow3_binary64`
15×	`exp-prod_binary64`
14×	`distribute-rgt-out_binary64`
12×	`cube-mult_binary64`
11×	`*-rgt-identity_binary64`
10×	`log-prod_binary64`
7×	`div-sub_binary64` `difference-of-squares_binary64` `distribute-rgt-neg-out_binary64`
6×	`distribute-rgt-out--_binary64`
5×	`log-div_binary64` `count-2_binary64` `associate-+r-_binary64`
4×	`unpow2_binary64` `pow-plus_binary64` `cube-div_binary64` `*-lft-identity_binary64` `distribute-neg-frac_binary64` `distribute-lft-out_binary64`
3×	`/-rgt-identity_binary64`
2×	`pow-base-1_binary64` `div-exp_binary64` `prod-exp_binary64` `exp-sum_binary64` `cube-unmult_binary64` `difference-of-sqr-1_binary64`
1×	`rec-exp_binary64` `1-exp_binary64` `cube-neg_binary64` `rem-3cbrt-lft_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `*-inverses_binary64` `cancel-sign-sub_binary64` `distribute-rgt1-in_binary64` `associate-+l-_binary64` `associate-+l+_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` `pow-base-0_binary64` `unpow1/3_binary64` `unpow1/2_binary64` `exp-to-pow_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_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` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `rem-sqrt-square_binary64` `unsub-neg_binary64` `mul-1-neg_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` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

186 → 390

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	533	11668
1	1667	10923

prune5.0s (6.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	390	0	390
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	390	9	399

Error

0.4b

Counts

399 → 9

Compiler

Compiled 52126 to 30425 computations (41.6% saved)

regimes5.0s (6.3%)

Accuracy

Total 0.2b remaining (37.4%)

Threshold costs 0.2b (37.4%)

Compiler

Compiled 96696 to 62452 computations (35.4% saved)

bsearch0.0ms (0%)

simplify13.0ms (0%)

Algorithm

1×	egg-herbie

Rules

23×	`*-commutative_binary64` `+-commutative_binary64`
14×	`sub-neg_binary64`
9×	`neg-mul-1_binary64` `neg-sub0_binary64`
4×	`distribute-rgt-neg-in_binary64`
3×	`distribute-lft-neg-in_binary64`
2×	`unsub-neg_binary64` `cancel-sign-sub-inv_binary64` `distribute-neg-in_binary64`
1×	`1-exp_binary64` `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` `exp-1-e_binary64` `exp-0_binary64` `sqr-abs_binary64` `sqr-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-rgt-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	181
1	82	181
2	104	181
3	126	181
4	139	181
5	145	181
6	147	181

Proof

(+ f64 h0 (+ f64 (+ f64 (* f64 (+ f64 (* f64 h0 h0) 1) (+ f64 (/ f64 (* f64 (- f64 (/ f64 (- f64 (+ f64 (* f64 h0 (* f64 h0 3)) (* f64 2 h1)) h0) (+ f64 (* f64 h0 h0) 1)) 3) (* f64 (- f64 (+ f64 (* f64 h0 (* f64 h0 3)) (* f64 2 h1)) h0) (* f64 h0 2))) (+ f64 (* f64 h0 h0) 1)) (* f64 h0 (* f64 h0 (- f64 (/ f64 (=> (* f64 4 (- f64 (+ f64 (* f64 h0 (* f64 h0 3)) (* f64 2 h1)) h0))) (+ f64 (* f64 h0 h0) 1)) 6))))) (+ f64 (/ f64 (- f64 (* f64 9 (pow f64 h0 4)) (* f64 3 (pow f64 h0 3))) (+ f64 (* f64 h0 h0) 1)) (* f64 h0 (* f64 h0 h0)))) (+ f64 h0 (* f64 3 (/ f64 (- f64 (* f64 h0 (* f64 h0 3)) (+ f64 (* f64 2 h1) h0)) (+ f64 (* f64 h0 h0) 1))))))
*-commutative_binary64 =>
(+ f64 h0 (+ f64 (+ f64 (* f64 (+ f64 (* f64 h0 h0) 1) (+ f64 (/ f64 (* f64 (- f64 (/ f64 (- f64 (+ f64 (* f64 h0 (* f64 h0 3)) (* f64 2 h1)) h0) (+ f64 (* f64 h0 h0) 1)) 3) (* f64 (- f64 (+ f64 (* f64 h0 (* f64 h0 3)) (* f64 2 h1)) h0) (* f64 h0 2))) (+ f64 (* f64 h0 h0) 1)) (* f64 h0 (* f64 h0 (- f64 (/ f64 (* f64 (- f64 (+ f64 (* f64 h0 (* f64 h0 3)) (* f64 2 h1)) h0) 4) (+ f64 (* f64 h0 h0) 1)) 6))))) (+ f64 (/ f64 (- f64 (* f64 9 (pow f64 h0 4)) (* f64 3 (pow f64 h0 3))) (+ f64 (* f64 h0 h0) 1)) (* f64 h0 (* f64 h0 h0)))) (+ f64 h0 (* f64 3 (/ f64 (- f64 (* f64 h0 (* f64 h0 3)) (=> (+ f64 (* f64 2 h1) h0))) (+ f64 (* f64 h0 h0) 1))))))
+-commutative_binary64 =>
(+ f64 h0 (+ f64 (+ f64 (* f64 (+ f64 (* f64 h0 h0) 1) (+ f64 (/ f64 (* f64 (- f64 (/ f64 (- f64 (+ f64 (* f64 h0 (* f64 h0 3)) (* f64 2 h1)) h0) (+ f64 (* f64 h0 h0) 1)) 3) (* f64 (- f64 (+ f64 (* f64 h0 (* f64 h0 3)) (* f64 2 h1)) h0) (* f64 h0 2))) (+ f64 (* f64 h0 h0) 1)) (* f64 h0 (* f64 h0 (- f64 (/ f64 (* f64 (- f64 (+ f64 (* f64 h0 (* f64 h0 3)) (* f64 2 h1)) h0) 4) (+ f64 (* f64 h0 h0) 1)) 6))))) (+ f64 (/ f64 (- f64 (* f64 9 (pow f64 h0 4)) (* f64 3 (pow f64 h0 3))) (+ f64 (* f64 h0 h0) 1)) (* f64 h0 (* f64 h0 h0)))) (+ f64 h0 (* f64 3 (/ f64 (- f64 (* f64 h0 (* f64 h0 3)) (+ f64 h0 (* f64 2 h1))) (+ f64 (* f64 h0 h0) 1))))))

end0.0ms (0%)

sample15.4s (19.4%)

Algorithm

1×

intervals

Results

1.5s	7100×	body	128	valid
1.2s	5765×	body	128	invalid
266.0ms	295×	body	1024	valid
237.0ms	361×	body	512	valid
106.0ms	244×	body	256	valid

Compiler

Compiled 24357 to 15731 computations (35.4% saved)

Details

analyze2.1s (2.7%)

sample145.0ms (0.2%)

simplify246.0ms (0.3%)

prune49.0ms (0.1%)

localize45.0ms (0.1%)

rewrite1.7s (2.1%)

series4.2s (5.3%)

simplify1.6s (2%)

prune10.9s (13.7%)

localize48.0ms (0.1%)

rewrite1.2s (1.5%)

series4.0s (5.1%)

simplify1.2s (1.5%)

prune6.3s (7.9%)

localize38.0ms (0%)

rewrite1.0s (1.3%)

series5.2s (6.6%)

simplify1.5s (1.8%)

prune4.7s (6%)

localize37.0ms (0%)

rewrite1.0s (1.3%)

series5.3s (6.6%)

simplify1.5s (1.9%)

prune5.0s (6.3%)

regimes5.0s (6.3%)

bsearch0.0ms (0%)

simplify13.0ms (0%)

end0.0ms (0%)

sample15.4s (19.4%)

Profiling