Details

analyze376.0ms (5.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5348	82
0	2	2
1	2	2

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)

sample63.0ms (1%)

Algorithm

1×

intervals

Results

28.0ms	71×	body	1024	valid
11.0ms	140×	body	128	valid
6.0ms	24×	body	512	valid
5.0ms	9×	body	2048	valid
2.0ms	12×	body	256	valid
1.0ms	12×	body	128	overflowed
0.0ms	5×	body	128	invalid

Compiler

Compiled 59 to 53 computations (10.2% saved)

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5212	41

prune7.0ms (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

Error

29.4b

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	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
0.0b	(*.f64 (-.f64 1 eps) x)
0.0b	(*.f64 (+.f64 1 eps) x)
1.9b	(-.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)))))

rewrite79.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64_769`
76×	`exp-neg_binary64_807` `frac-times_binary64_770`
57×	`exp-diff_binary64_808` `neg-sub0_binary64_755`
42×	`associate-*l/_binary64_703`
38×	`associate-*r/_binary64_702`
31×	`flip3-+_binary64_763` `flip-+_binary64_734`
29×	`flip--_binary64_735` `flip3--_binary64_764`
19×	`un-div-inv_binary64_758` `add-sqr-sqrt_binary64_782`
18×	`*-un-lft-identity_binary64_760`
15×	`associate-l_binary64_701`
10×	`add-cube-cbrt_binary64_795` `add-cbrt-cube_binary64_796` `pow1_binary64_821`
9×	`add-exp-log_binary64_798` `associate-r_binary64_700`
6×	`add-log-exp_binary64_799`
3×	`unswap-sqr_binary64_728` `distribute-lft-out_binary64_711` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `*-commutative_binary64_691`
2×	`difference-of-squares_binary64_729`
1×	`diff-log_binary64_852` `cancel-sign-sub-inv_binary64_726` `div-inv_binary64_757` `distribute-lft-out--_binary64_712` `sub-neg_binary64_753`

Counts

4 → 166

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)))))
13.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
7.0ms	(*.f64 (-.f64 1 eps) x)
7.0ms	(*.f64 (+.f64 1 eps) x)

series188.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(-.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)))))
28.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
21.0ms	(*.f64 (-.f64 1 eps) x)
17.0ms	(*.f64 (+.f64 1 eps) x)

simplify132.0ms (2%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5003	8781

prune563.0ms (8.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	177	2	179

Error

0.5b

Counts

179 → 2

Compiler

Compiled 8264 to 6349 computations (23.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
6.6b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_782`
12×	`associate-l_binary64_701`
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-r_binary64_700`
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:

9.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
6.0ms	(*.f64 (pow.f64 x 3) 2/3)

series42.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

25.0ms	(*.f64 (pow.f64 x 3) 2/3)
18.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

simplify57.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4879	687
1	4879	687

prune56.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	51	3	54

Error

0.5b

Counts

54 → 3

Compiler

Compiled 996 to 737 computations (26% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
0.5b	(exp.f64 (log.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))))
6.6b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
11.4b	(log.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_782`
12×	`associate-l_binary64_701`
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-r_binary64_700` `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 (pow.f64 x 3) 2/3) 2) (.f64 x x))))
8.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
8.0ms	(log.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
7.0ms	(*.f64 (pow.f64 x 3) 2/3)

series107.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(exp.f64 (log.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))))
25.0ms	(*.f64 (pow.f64 x 3) 2/3)
22.0ms	(log.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
17.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

simplify84.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4901	1662
1	4901	1662

prune110.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	91	3	94

Error

0.5b

Counts

94 → 3

Compiler

Compiled 1986 to 1507 computations (24.1% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 (-.f64 1 eps) x)))
0.0b	(*.f64 (-.f64 1 eps) x)
0.0b	(*.f64 (+.f64 1 eps) x)
3.1b	(-.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))))

rewrite54.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64_760`
25×	`add-sqr-sqrt_binary64_782`
18×	`add-cube-cbrt_binary64_795`
15×	`times-frac_binary64_766`
10×	`add-cbrt-cube_binary64_796` `associate-l_binary64_701`
9×	`distribute-lft-out_binary64_711` `add-exp-log_binary64_798` `frac-sub_binary64_769`
8×	`pow1_binary64_821`
6×	`associate-l/_binary64_703` `add-log-exp_binary64_799` `associate-r*_binary64_700`
5×	`div-inv_binary64_757` `associate-/l*_binary64_705` `flip--_binary64_735` `flip3--_binary64_764`
4×	`exp-neg_binary64_807` `frac-times_binary64_770`
3×	`associate-/r*_binary64_704` `exp-diff_binary64_808` `neg-sub0_binary64_755`
2×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `flip3-+_binary64_763` `associate-/l/_binary64_707` `difference-of-squares_binary64_729` `flip-+_binary64_734` `associate-r/_binary64_702` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `-commutative_binary64_691`
1×	`diff-log_binary64_852` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `cancel-sign-sub-inv_binary64_726` `distribute-lft-out--_binary64_712` `div-exp_binary64_811` `clear-num_binary64_759` `sub-neg_binary64_753` `un-div-inv_binary64_758`

Counts

4 → 102

Calls

4 calls:

19.0ms	(-.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))))
11.0ms	(/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 (-.f64 1 eps) x)))
7.0ms	(*.f64 (-.f64 1 eps) x)
6.0ms	(*.f64 (+.f64 1 eps) x)

series270.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

188.0ms	(-.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))))
44.0ms	(/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 (-.f64 1 eps) x)))
21.0ms	(*.f64 (-.f64 1 eps) x)
16.0ms	(*.f64 (+.f64 1 eps) x)

simplify134.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4975	2909
1	4975	2909

prune219.0ms (3.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	113	4	117

Error

0.4b

Counts

117 → 4

Compiler

Compiled 4138 to 3215 computations (22.3% saved)

regimes528.0ms (8.1%)

Accuracy

Total 0.5b remaining (58.2%)

Threshold costs 0.5b (58.2%)

Compiler

Compiled 6384 to 5320 computations (16.7% saved)

bsearch93.0ms (1.4%)

Steps

Iters	Range		Point
10	2.6253646371756867e-17	43.443390296362715	2.861739657050829

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	72	76
1	72	76

end0.0ms (0%)

sample3.1s (48.4%)

Algorithm

1×

intervals

Results

796.0ms	1938×	body	1024	valid
354.0ms	4328×	body	128	valid
259.0ms	1059×	body	512	valid
133.0ms	195×	body	2048	valid
76.0ms	480×	body	256	valid
18.0ms	216×	body	128	invalid
14.0ms	178×	body	128	overflowed
9.0ms	23×	body	1024	invalid
5.0ms	11×	body	512	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 1647 to 1370 computations (16.8% saved)

Details

analyze376.0ms (5.8%)

sample63.0ms (1%)

simplify71.0ms (1.1%)

prune7.0ms (0.1%)

localize17.0ms (0.3%)

rewrite79.0ms (1.2%)

series188.0ms (2.9%)

simplify132.0ms (2%)

prune563.0ms (8.7%)

localize8.0ms (0.1%)

rewrite18.0ms (0.3%)

series42.0ms (0.7%)

simplify57.0ms (0.9%)

prune56.0ms (0.9%)

localize13.0ms (0.2%)

rewrite38.0ms (0.6%)

series107.0ms (1.6%)

simplify84.0ms (1.3%)

prune110.0ms (1.7%)

localize19.0ms (0.3%)

rewrite54.0ms (0.8%)

series270.0ms (4.2%)

simplify134.0ms (2.1%)

prune219.0ms (3.4%)

regimes528.0ms (8.1%)

bsearch93.0ms (1.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.1s (48.4%)

Profiling