Details

analyze463.0ms (4.5%)

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
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

Compiler

Compiled 30 to 26 computations (13.3% saved)

sample128.0ms (1.2%)

Algorithm

1×

intervals

Results

48.0ms	55×	body	1024	valid
25.0ms	136×	body	128	valid
19.0ms	38×	body	512	valid
12.0ms	7×	body	2048	valid
6.0ms	20×	body	256	valid
1.0ms	6×	body	128	overflowed
1.0ms	3×	body	128	invalid

Compiler

Compiled 59 to 53 computations (10.2% saved)

simplify423.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4908	41
1	4908	41

prune9.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 30.1b

Counts

2 → 1

Compiler

Compiled 56 to 48 computations (14.3% saved)

localize37.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
2.4b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite164.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64_86`
78×	`exp-neg_binary64_121`
76×	`frac-times_binary64_87`
59×	`exp-diff_binary64_122` `neg-sub0_binary64_72`
38×	`associate-l/_binary64_22` `associate-r/_binary64_21`
31×	`flip--_binary64_52` `flip3--_binary64_81`
27×	`flip-+_binary64_51` `flip3-+_binary64_80`
25×	`add-sqr-sqrt_binary64_98`
19×	`un-div-inv_binary64_75`
17×	`*-un-lft-identity_binary64_77`
14×	`associate-l_binary64_20`
12×	`exp-prod_binary64_126`
10×	`add-log-exp_binary64_113`
8×	`add-cube-cbrt_binary64_109`
6×	`add-cbrt-cube_binary64_110` `times-frac_binary64_83` `pow1_binary64_135` `difference-of-squares_binary64_46`
5×	`add-exp-log_binary64_112`
4×	`rem-exp-log_binary64_114`
3×	`difference-of-sqr-1_binary64_47` `associate-r_binary64_19`
2×	`distribute-lft-neg-in_binary64_36` `distribute-lft-out--_binary64_31` `neg-mul-1_binary64_73` `distribute-rgt-neg-in_binary64_37` `neg-log_binary64_167`
1×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `sub-neg_binary64_70` `unswap-sqr_binary64_45` `prod-exp_binary64_123` `*-commutative_binary64_10` `diff-log_binary64_166` `div-inv_binary64_74`

Counts

4 → 164

Calls

4 calls:

41.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
35.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
8.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
7.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

series774.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

498.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
145.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
71.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
59.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))

simplify245.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4966	8717
1	4966	8717

prune965.0ms (9.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	171	5	176
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	172	5	177

Merged error: 0.8b

Counts

177 → 5

Compiler

Compiled 8240 to 6402 computations (22.3% saved)

localize17.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 2/3 (pow.f64 x 3))
5.6b	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_98`
12×	`associate-r_binary64_19`
7×	`add-exp-log_binary64_112` `add-log-exp_binary64_113`
6×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
4×	`add-cbrt-cube_binary64_110` `unswap-sqr_binary64_45` `unpow-prod-down_binary64_153` `cube-prod_binary64_102`
3×	`associate-l_binary64_20` `prod-exp_binary64_123`
2×	`sqr-pow_binary64_49` `pow1_binary64_135` `diff-log_binary64_166`
1×	`pow-to-exp_binary64_143` `cbrt-unprod_binary64_107` `associate--l+_binary64_16` `sub-neg_binary64_70` `pow-exp_binary64_142` `cube-mult_binary64_104` `flip--_binary64_52` `difference-of-squares_binary64_46` `*-commutative_binary64_10` `flip3--_binary64_81` `sum-log_binary64_165` `unpow3_binary64_140`

Counts

2 → 45

Calls

2 calls:

17.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
13.0ms	(*.f64 2/3 (pow.f64 x 3))

series164.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

100.0ms	(*.f64 2/3 (pow.f64 x 3))
65.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

simplify162.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (139.0ms)

Iter	Nodes	Cost
0	4948	664
1	4948	664

prune136.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	48	8	56

Merged error: 0.8b

Counts

56 → 8

Compiler

Compiled 1182 to 895 computations (24.3% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3)) (*.f64 (pow.f64 x 3) (cbrt.f64 2/3)))
0.1b	(*.f64 (pow.f64 x 3) (cbrt.f64 2/3))
1.0b	(*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))
5.6b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3)) (.f64 (pow.f64 x 3) (cbrt.f64 2/3))) 2) (.f64 x x))

rewrite110.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_98`
35×	`add-exp-log_binary64_112`
23×	`cbrt-prod_binary64_105`
22×	`prod-exp_binary64_123`
19×	`associate-l_binary64_20`
17×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
16×	`pow1_binary64_135`
13×	`associate-r_binary64_19`
12×	`unswap-sqr_binary64_45`
11×	`add-cbrt-cube_binary64_110`
10×	`cbrt-unprod_binary64_107`
9×	`add-log-exp_binary64_113`
6×	`swap-sqr_binary64_44` `pow1/3_binary64_156`
5×	`pow-prod-down_binary64_145` `unpow-prod-down_binary64_153` `cube-prod_binary64_102`
3×	`pow-to-exp_binary64_143` `sqr-pow_binary64_49` `pow-exp_binary64_142` `*-commutative_binary64_10`
2×	`pow-sqr_binary64_50` `pow-prod-up_binary64_144` `diff-log_binary64_166`
1×	`pow2_binary64_155` `associate--l+_binary64_16` `pow-plus_binary64_137` `sub-neg_binary64_70` `cube-mult_binary64_104` `flip--_binary64_52` `difference-of-squares_binary64_46` `flip3--_binary64_81` `sum-log_binary64_165` `unpow3_binary64_140`

Counts

4 → 116

Calls

4 calls:

31.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3)) (.f64 (pow.f64 x 3) (cbrt.f64 2/3))) 2) (.f64 x x))
28.0ms	(.f64 (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3)) (*.f64 (pow.f64 x 3) (cbrt.f64 2/3)))
16.0ms	(*.f64 (pow.f64 x 3) (cbrt.f64 2/3))
12.0ms	(*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))

series482.0ms (4.7%)

Counts

4 → 10

Calls

4 calls:

228.0ms	(.f64 (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3)) (*.f64 (pow.f64 x 3) (cbrt.f64 2/3)))
145.0ms	(*.f64 (pow.f64 x 3) (cbrt.f64 2/3))
109.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3)) (.f64 (pow.f64 x 3) (cbrt.f64 2/3))) 2) (.f64 x x))
0.0ms	(*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))

simplify98.0ms (1%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5343	1523

prune344.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	126	8	134

Merged error: 0.8b

Counts

134 → 8

Compiler

Compiled 3048 to 2455 computations (19.5% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3)
0.1b	(*.f64 2/3 (pow.f64 x 3))
3.8b	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3))
5.6b	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

rewrite90.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_98`
14×	`cbrt-prod_binary64_105` `add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
12×	`unpow-prod-down_binary64_153` `associate-r_binary64_19` `cube-prod_binary64_102`
10×	`add-exp-log_binary64_112`
9×	`add-log-exp_binary64_113`
7×	`add-cbrt-cube_binary64_110`
5×	`pow1_binary64_135` `difference-of-squares_binary64_46`
4×	`cube-div_binary64_103` `sqr-pow_binary64_49` `unswap-sqr_binary64_45`
3×	`associate-l_binary64_20` `cube-mult_binary64_104` `flip--_binary64_52` `pow-unpow_binary64_151` `prod-exp_binary64_123` `flip3--_binary64_81` `unpow3_binary64_140`
2×	`pow-to-exp_binary64_143` `pow-exp_binary64_142` `cbrt-div_binary64_106` `diff-log_binary64_166`
1×	`rem-cbrt-cube_binary64_100` `rem-cube-cbrt_binary64_99` `cbrt-unprod_binary64_107` `associate--l+_binary64_16` `sub-neg_binary64_70` `*-commutative_binary64_10` `pow1/3_binary64_156` `pow-pow_binary64_146` `sum-log_binary64_165`

Counts

4 → 97

Calls

4 calls:

21.0ms	(pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3)
20.0ms	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3))
17.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
14.0ms	(*.f64 2/3 (pow.f64 x 3))

series295.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(*.f64 2/3 (pow.f64 x 3))
73.0ms	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3))
65.0ms	(pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3)
62.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

simplify150.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4946	2144
1	4946	2144

prune265.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	1	5	6
Picked	1	0	1
Done	1	0	1
Total	109	8	117

Merged error: 0.8b

Counts

117 → 8

Compiler

Compiled 2407 to 1831 computations (23.9% saved)

regimes123.0ms (1.2%)

Compiler: Compiled 574 to 500 computations (12.9% saved)

bsearch175.0ms (1.7%)

Steps

Iters	Range		Point
10	0.0005232170036747243	1725021723.2365746	10.306908003704974

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	239	77
1	239	77

end0.0ms (0%)

sample4.4s (42.5%)

Algorithm

1×

intervals

Results

1.7s	1952×	body	1024	valid
685.0ms	4274×	body	128	valid
512.0ms	1017×	body	512	valid
312.0ms	223×	body	2048	valid
174.0ms	534×	body	256	valid
36.0ms	219×	body	128	invalid
31.0ms	205×	body	128	overflowed
14.0ms	17×	body	1024	invalid
4.0ms	6×	body	512	invalid
1.0ms	4×	body	256	invalid

Compiler

Compiled 365 to 316 computations (13.4% saved)

Details

analyze463.0ms (4.5%)

sample128.0ms (1.2%)

simplify423.0ms (4.1%)

prune9.0ms (0.1%)

localize37.0ms (0.4%)

rewrite164.0ms (1.6%)

series774.0ms (7.5%)

simplify245.0ms (2.4%)

prune965.0ms (9.4%)

localize17.0ms (0.2%)

rewrite38.0ms (0.4%)

series164.0ms (1.6%)

simplify162.0ms (1.6%)

prune136.0ms (1.3%)

localize24.0ms (0.2%)

rewrite110.0ms (1.1%)

series482.0ms (4.7%)

simplify98.0ms (1%)

prune344.0ms (3.3%)

localize22.0ms (0.2%)

rewrite90.0ms (0.9%)

series295.0ms (2.9%)

simplify150.0ms (1.5%)

prune265.0ms (2.6%)

regimes123.0ms (1.2%)

bsearch175.0ms (1.7%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample4.4s (42.5%)

Profiling