Details

analyze231.0ms (3.6%)

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)

sample65.0ms (1%)

Algorithm

1×

intervals

Results

28.0ms	68×	body	1024	valid
11.0ms	133×	body	128	valid
8.0ms	35×	body	512	valid
7.0ms	8×	body	2048	valid
2.0ms	12×	body	256	valid
0.0ms	6×	body	128	invalid
0.0ms	1×	body	1024	invalid
0.0ms	3×	body	128	overflowed

Compiler

Compiled 59 to 53 computations (10.2% saved)

simplify158.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5212	41

prune4.0ms (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: 30.7b

Counts

2 → 1

Compiler

Compiled 56 to 48 computations (14.3% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
0.0b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
3.4b	(-.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)))))

rewrite85.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`exp-neg_binary64_807` `frac-sub_binary64_769`
80×	`frac-times_binary64_770`
61×	`exp-diff_binary64_808` `neg-sub0_binary64_755`
40×	`associate-l/_binary64_703` `associate-r/_binary64_702`
31×	`flip--_binary64_735` `flip3--_binary64_764`
30×	`flip3-+_binary64_763` `flip-+_binary64_734`
28×	`add-sqr-sqrt_binary64_782`
21×	`*-un-lft-identity_binary64_760`
20×	`un-div-inv_binary64_758`
19×	`associate-l_binary64_701`
9×	`add-cube-cbrt_binary64_795`
8×	`add-log-exp_binary64_799` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
6×	`exp-prod_binary64_812` `add-exp-log_binary64_798` `difference-of-squares_binary64_729` `associate-r_binary64_700` `times-frac_binary64_766`
3×	`difference-of-sqr-1_binary64_730`
2×	`unswap-sqr_binary64_728` `distribute-lft-out_binary64_711` `prod-exp_binary64_809` `rem-exp-log_binary64_800` `div-inv_binary64_757` `distribute-lft-out--_binary64_712` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `*-commutative_binary64_691`
1×	`neg-mul-1_binary64_756` `diff-log_binary64_852` `distribute-lft-neg-in_binary64_717` `cancel-sign-sub-inv_binary64_726` `neg-log_binary64_853` `distribute-rgt-neg-in_binary64_718` `sub-neg_binary64_753`

Counts

4 → 177

Calls

4 calls:

19.0ms	(-.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)))))
19.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
13.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
4.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))

series218.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

137.0ms	(-.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)))))
36.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
28.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
17.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))

simplify129.0ms (2%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4982	9336
1	4982	9336

prune547.0ms (8.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	187	3	190

Merged error: 0.3b

Counts

190 → 3

Compiler

Compiled 8735 to 6729 computations (23% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 2/3 (pow.f64 x 3))
5.4b	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_782`
12×	`associate-r_binary64_700`
7×	`add-exp-log_binary64_798` `add-log-exp_binary64_799`
6×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
4×	`unswap-sqr_binary64_728` `add-cbrt-cube_binary64_796` `cube-prod_binary64_788` `unpow-prod-down_binary64_839`
3×	`prod-exp_binary64_809` `associate-l_binary64_701`
2×	`diff-log_binary64_852` `sqr-pow_binary64_732` `pow1_binary64_821`
1×	`cube-mult_binary64_790` `unpow3_binary64_826` `cancel-sign-sub-inv_binary64_726` `pow-exp_binary64_828` `difference-of-squares_binary64_729` `pow-to-exp_binary64_829` `sum-log_binary64_851` `cbrt-unprod_binary64_793` `associate--l+_binary64_697` `sub-neg_binary64_753` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`

Counts

2 → 46

Calls

2 calls:

8.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
7.0ms	(*.f64 2/3 (pow.f64 x 3))

series44.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

27.0ms	(*.f64 2/3 (pow.f64 x 3))
18.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

simplify60.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4912	670
1	4912	670

prune59.0ms (0.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	51	4	55

Merged error: 0.2b

Counts

55 → 4

Compiler

Compiled 1046 to 775 computations (25.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 2/3 (pow.f64 x 3))
0.4b	(exp.f64 (log.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))))
5.4b	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
9.7b	(log.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_782`
12×	`associate-r_binary64_700`
11×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795`
10×	`add-exp-log_binary64_798`
9×	`add-log-exp_binary64_799`
8×	`log-prod_binary64_846`
6×	`add-cbrt-cube_binary64_796` `pow1_binary64_821`
4×	`log-div_binary64_847` `unswap-sqr_binary64_728` `exp-prod_binary64_812` `exp-sum_binary64_806` `cube-prod_binary64_788` `unpow-prod-down_binary64_839`
3×	`prod-exp_binary64_809` `difference-of-squares_binary64_729` `associate-l_binary64_701` `flip--_binary64_735` `flip3--_binary64_764`
2×	`diff-log_binary64_852` `exp-diff_binary64_808` `log-pow_binary64_849` `sqr-pow_binary64_732`
1×	`cube-mult_binary64_790` `unpow3_binary64_826` `cancel-sign-sub-inv_binary64_726` `pow-exp_binary64_828` `rem-exp-log_binary64_800` `pow-to-exp_binary64_829` `sum-log_binary64_851` `rem-log-exp_binary64_801` `cbrt-unprod_binary64_793` `associate--l+_binary64_697` `sub-neg_binary64_753` `*-commutative_binary64_691`

Counts

4 → 79

Calls

4 calls:

9.0ms	(exp.f64 (log.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))))
8.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
7.0ms	(log.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))
7.0ms	(*.f64 2/3 (pow.f64 x 3))

series116.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(exp.f64 (log.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))))
27.0ms	(*.f64 2/3 (pow.f64 x 3))
21.0ms	(log.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)))
17.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4823	1639
1	4823	1639

prune114.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	91	4	95

Merged error: 0.2b

Counts

95 → 4

Compiler

Compiled 2051 to 1561 computations (23.9% saved)

localize10.0ms (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))
3.0b	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3))
5.4b	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_782`
14×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `cbrt-prod_binary64_791`
12×	`associate-r_binary64_700` `cube-prod_binary64_788` `unpow-prod-down_binary64_839`
10×	`add-exp-log_binary64_798`
9×	`add-log-exp_binary64_799`
7×	`add-cbrt-cube_binary64_796`
5×	`difference-of-squares_binary64_729` `pow1_binary64_821`
4×	`unswap-sqr_binary64_728` `cube-div_binary64_789` `sqr-pow_binary64_732`
3×	`cube-mult_binary64_790` `prod-exp_binary64_809` `unpow3_binary64_826` `associate-l_binary64_701` `pow-unpow_binary64_837` `flip--_binary64_735` `flip3--_binary64_764`
2×	`diff-log_binary64_852` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `cbrt-div_binary64_792`
1×	`pow1/3_binary64_842` `rem-cbrt-cube_binary64_784` `cancel-sign-sub-inv_binary64_726` `rem-cube-cbrt_binary64_783` `sum-log_binary64_851` `cbrt-unprod_binary64_793` `associate--l+_binary64_697` `sub-neg_binary64_753` `*-commutative_binary64_691` `pow-pow_binary64_832`

Counts

4 → 98

Calls

4 calls:

9.0ms	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3))
9.0ms	(pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3)
8.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
7.0ms	(*.f64 2/3 (pow.f64 x 3))

series81.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

23.0ms	(*.f64 2/3 (pow.f64 x 3))
20.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
19.0ms	(pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3)
19.0ms	(cbrt.f64 (pow.f64 (-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x)) 3))

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5080	2168

prune133.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	110	4	114

Merged error: 0.2b

Counts

114 → 4

Compiler

Compiled 2434 to 1836 computations (24.6% saved)

regimes580.0ms (8.9%)

Compiler: Compiled 8464 to 7060 computations (16.6% saved)

bsearch86.0ms (1.3%)

Steps

Iters	Range		Point
9	1.8661842019580433e-05	1.9347424316766901	1.9184223926600088

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	215	95
1	215	95

end0.0ms (0%)

sample3.5s (54%)

Algorithm

1×

intervals

Results

829.0ms	2012×	body	1024	valid
347.0ms	4359×	body	128	valid
238.0ms	967×	body	512	valid
137.0ms	205×	body	2048	valid
75.0ms	457×	body	256	valid
21.0ms	225×	body	128	invalid
13.0ms	173×	body	128	overflowed
8.0ms	21×	body	1024	invalid
1.0ms	4×	body	512	invalid
1.0ms	4×	body	256	invalid

Compiler

Compiled 2179 to 1819 computations (16.5% saved)

Details

analyze231.0ms (3.6%)

sample65.0ms (1%)

simplify158.0ms (2.4%)

prune4.0ms (0.1%)

localize17.0ms (0.3%)

rewrite85.0ms (1.3%)

series218.0ms (3.4%)

simplify129.0ms (2%)

prune547.0ms (8.4%)

localize8.0ms (0.1%)

rewrite18.0ms (0.3%)

series44.0ms (0.7%)

simplify60.0ms (0.9%)

prune59.0ms (0.9%)

localize11.0ms (0.2%)

rewrite37.0ms (0.6%)

series116.0ms (1.8%)

simplify70.0ms (1.1%)

prune114.0ms (1.8%)

localize10.0ms (0.2%)

rewrite41.0ms (0.6%)

series81.0ms (1.2%)

simplify63.0ms (1%)

prune133.0ms (2%)

regimes580.0ms (8.9%)

bsearch86.0ms (1.3%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample3.5s (54%)

Profiling