Details

analyze1.1s (11.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
1.6%	98.2%	0.2%	9
2.3%	97.5%	0.2%	10
11.7%	88.1%	0.2%	11
13.1%	74.3%	12.7%	12
16.1%	70.5%	13.5%	13
18.6%	68%	13.5%	14

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample72.0ms (0.8%)

Algorithm

1×

intervals

Results

18.0ms	41×	body	1024	valid
12.0ms	52×	body	512	valid
10.0ms	129×	body	128	valid
9.0ms	9×	body	2048	valid
4.0ms	25×	body	256	valid
3.0ms	53×	body	128	nan
1.0ms	23×	body	128	overflowed
1.0ms	6×	body	512	nan
1.0ms	4×	body	1024	nan
0.0ms	1×	body	512	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 27 to 29 computations (-7.4% saved)

simplify511.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (345.0ms)

Iter	Nodes	Cost
0	3706	20
1	3706	20

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 25.6b

Counts

2 → 1

Compiler

Compiled 26 to 24 computations (7.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 y (exp.f64 z))
0.0b	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
2.0b	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))
2.4b	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_10421`
17×	`add-cube-cbrt_binary64_10434` `*-un-lft-identity_binary64_10399`
12×	`times-frac_binary64_10405`
11×	`pow1_binary64_10460`
9×	`add-log-exp_binary64_10438`
8×	`add-exp-log_binary64_10437` `add-cbrt-cube_binary64_10435`
5×	`log-pow_binary64_10488`
4×	`associate-/l*_binary64_10344` `log-div_binary64_10486` `associate-+l+_binary64_10332`
3×	`associate-/r_binary64_10343` `flip3-+_binary64_10402` `log-prod_binary64_10485` `flip-+_binary64_10373` `cancel-sign-sub-inv_binary64_10365` `associate-l_binary64_10340` `associate-r*_binary64_10339`
2×	`sum-log_binary64_10490` `div-sub_binary64_10404`
1×	`cbrt-undiv_binary64_10433` `sub-neg_binary64_10392` `frac-2neg_binary64_10410` `*-commutative_binary64_10330` `div-inv_binary64_10396` `unswap-sqr_binary64_10367` `cbrt-unprod_binary64_10432` `prod-exp_binary64_10448` `+-commutative_binary64_10329` `rem-log-exp_binary64_10440` `associate-+l-_binary64_10334` `pow-prod-down_binary64_10470` `diff-log_binary64_10491` `div-exp_binary64_10450` `clear-num_binary64_10398`

Counts

4 → 82

Calls

4 calls:

10.0ms	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
9.0ms	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))
7.0ms	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))
6.0ms	(*.f64 y (exp.f64 z))

series623.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

388.0ms	(/.f64 (log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))) t)
136.0ms	(log.f64 (+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z))))
57.0ms	(+.f64 (-.f64 1 y) (*.f64 y (exp.f64 z)))
41.0ms	(*.f64 y (exp.f64 z))

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4917	1998
1	4917	1998

prune358.0ms (3.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	88	6	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	6	95

Merged error: 4.9b

Counts

95 → 6

Compiler

Compiled 6356 to 4413 computations (30.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 y (exp.f64 z))
0.0b	(/.f64 (log.f64 (-.f64 1 (-.f64 y (*.f64 y (exp.f64 z))))) t)
2.2b	(log.f64 (-.f64 1 (-.f64 y (*.f64 y (exp.f64 z)))))
4.0b	(-.f64 y (*.f64 y (exp.f64 z)))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_10421`
19×	`*-un-lft-identity_binary64_10399`
16×	`add-cube-cbrt_binary64_10434`
12×	`times-frac_binary64_10405`
11×	`pow1_binary64_10460`
8×	`add-exp-log_binary64_10437` `add-cbrt-cube_binary64_10435`
6×	`log-prod_binary64_10485` `add-log-exp_binary64_10438`
5×	`log-pow_binary64_10488`
4×	`associate-/l*_binary64_10344` `log-div_binary64_10486`
3×	`associate-/r_binary64_10343` `flip3--_binary64_10403` `associate-l_binary64_10340` `associate-r*_binary64_10339` `flip--_binary64_10374`
2×	`difference-of-squares_binary64_10368` `div-sub_binary64_10404`
1×	`cbrt-undiv_binary64_10433` `sub-neg_binary64_10392` `frac-2neg_binary64_10410` `*-commutative_binary64_10330` `div-inv_binary64_10396` `unswap-sqr_binary64_10367` `cbrt-unprod_binary64_10432` `prod-exp_binary64_10448` `cancel-sign-sub-inv_binary64_10365` `rem-log-exp_binary64_10440` `pow-prod-down_binary64_10470` `diff-log_binary64_10491` `div-exp_binary64_10450` `distribute-lft-out--_binary64_10351` `clear-num_binary64_10398`

Counts

4 → 80

Calls

4 calls:

8.0ms	(/.f64 (log.f64 (-.f64 1 (-.f64 y (*.f64 y (exp.f64 z))))) t)
6.0ms	(*.f64 y (exp.f64 z))
5.0ms	(log.f64 (-.f64 1 (-.f64 y (*.f64 y (exp.f64 z)))))
3.0ms	(-.f64 y (*.f64 y (exp.f64 z)))

series627.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

396.0ms	(/.f64 (log.f64 (-.f64 1 (-.f64 y (*.f64 y (exp.f64 z))))) t)
140.0ms	(log.f64 (-.f64 1 (-.f64 y (*.f64 y (exp.f64 z)))))
55.0ms	(-.f64 y (*.f64 y (exp.f64 z)))
36.0ms	(*.f64 y (exp.f64 z))

simplify128.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4903	1949
1	4903	1949

prune125.0ms (1.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	90	2	92
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	92	6	98

Merged error: 4.9b

Counts

98 → 6

Compiler

Compiled 2481 to 1336 computations (46.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.3b	(-.f64 1 (exp.f64 z))
4.3b	(-.f64 1 (exp.f64 z))
6.8b	(log.f64 (+.f64 1 (.f64 y (+.f64 (-.f64 1 (exp.f64 z)) (.f64 y (pow.f64 (-.f64 1 (exp.f64 z)) 2))))))
7.5b	(log.f64 (+.f64 1 (pow.f64 (-.f64 (*.f64 y (exp.f64 z)) y) 3)))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64_10399`
14×	`add-sqr-sqrt_binary64_10421`
8×	`add-cube-cbrt_binary64_10434` `add-log-exp_binary64_10438`
7×	`log-prod_binary64_10485`
6×	`add-exp-log_binary64_10437` `pow1_binary64_10460` `cancel-sign-sub-inv_binary64_10365`
4×	`log-div_binary64_10486` `add-cbrt-cube_binary64_10435` `difference-of-squares_binary64_10368`
2×	`sub-neg_binary64_10392` `flip3-+_binary64_10402` `flip3--_binary64_10403` `flip-+_binary64_10373` `rem-log-exp_binary64_10440` `log-pow_binary64_10488` `diff-log_binary64_10491` `flip--_binary64_10374` `distribute-lft-out--_binary64_10351`
1×	`distribute-lft-out_binary64_10350`

Counts

4 → 63

Calls

4 calls:

13.0ms	(log.f64 (+.f64 1 (pow.f64 (-.f64 (*.f64 y (exp.f64 z)) y) 3)))
5.0ms	(-.f64 1 (exp.f64 z))
5.0ms	(-.f64 1 (exp.f64 z))
3.0ms	(log.f64 (+.f64 1 (.f64 y (+.f64 (-.f64 1 (exp.f64 z)) (.f64 y (pow.f64 (-.f64 1 (exp.f64 z)) 2))))))

series1.3s (13.9%)

Counts

4 → 12

Calls

4 calls:

643.0ms	(log.f64 (+.f64 1 (pow.f64 (-.f64 (*.f64 y (exp.f64 z)) y) 3)))
632.0ms	(log.f64 (+.f64 1 (.f64 y (+.f64 (-.f64 1 (exp.f64 z)) (.f64 y (pow.f64 (-.f64 1 (exp.f64 z)) 2))))))
20.0ms	(-.f64 1 (exp.f64 z))
18.0ms	(-.f64 1 (exp.f64 z))

simplify68.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5001	1912

prune211.0ms (2.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	72	9	81

Merged error: 4.8b

Counts

81 → 9

Compiler

Compiled 4679 to 3006 computations (35.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (*.f64 y (exp.f64 z)))
0.4b	(cbrt.f64 (*.f64 y (exp.f64 z)))
3.4b	(log.f64 (+.f64 (-.f64 1 y) (.f64 (.f64 (cbrt.f64 (.f64 y (exp.f64 z))) (cbrt.f64 (.f64 y (exp.f64 z)))) (cbrt.f64 (*.f64 y (exp.f64 z))))))
13.5b	(+.f64 (-.f64 1 y) (.f64 (.f64 (cbrt.f64 (.f64 y (exp.f64 z))) (cbrt.f64 (.f64 y (exp.f64 z)))) (cbrt.f64 (*.f64 y (exp.f64 z)))))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64_10438`
6×	`add-cube-cbrt_binary64_10434` `add-sqr-sqrt_binary64_10421` `*-un-lft-identity_binary64_10399`
5×	`add-exp-log_binary64_10437` `pow1_binary64_10460`
4×	`add-cbrt-cube_binary64_10435` `associate-+l+_binary64_10332`
3×	`log-prod_binary64_10485` `cancel-sign-sub-inv_binary64_10365`
2×	`cbrt-prod_binary64_10430` `log-div_binary64_10486` `sum-log_binary64_10490` `flip3-+_binary64_10402` `flip-+_binary64_10373` `pow1/3_binary64_10481`
1×	`sub-neg_binary64_10392` `+-commutative_binary64_10329` `rem-log-exp_binary64_10440` `associate-+l-_binary64_10334` `log-pow_binary64_10488` `diff-log_binary64_10491`

Counts

4 → 49

Calls

4 calls:

11.0ms	(+.f64 (-.f64 1 y) (.f64 (.f64 (cbrt.f64 (.f64 y (exp.f64 z))) (cbrt.f64 (.f64 y (exp.f64 z)))) (cbrt.f64 (*.f64 y (exp.f64 z)))))
10.0ms	(log.f64 (+.f64 (-.f64 1 y) (.f64 (.f64 (cbrt.f64 (.f64 y (exp.f64 z))) (cbrt.f64 (.f64 y (exp.f64 z)))) (cbrt.f64 (*.f64 y (exp.f64 z))))))
4.0ms	(cbrt.f64 (*.f64 y (exp.f64 z)))
4.0ms	(cbrt.f64 (*.f64 y (exp.f64 z)))

series522.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

174.0ms	(log.f64 (+.f64 (-.f64 1 y) (.f64 (.f64 (cbrt.f64 (.f64 y (exp.f64 z))) (cbrt.f64 (.f64 y (exp.f64 z)))) (cbrt.f64 (*.f64 y (exp.f64 z))))))
137.0ms	(cbrt.f64 (*.f64 y (exp.f64 z)))
129.0ms	(cbrt.f64 (*.f64 y (exp.f64 z)))
82.0ms	(+.f64 (-.f64 1 y) (.f64 (.f64 (cbrt.f64 (.f64 y (exp.f64 z))) (cbrt.f64 (.f64 y (exp.f64 z)))) (cbrt.f64 (*.f64 y (exp.f64 z)))))

simplify135.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	4856	1005
1	4856	1005

prune102.0ms (1.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	60	10	70

Merged error: 4.8b

Counts

70 → 10

Compiler

Compiled 2401 to 1212 computations (49.5% saved)

regimes286.0ms (3%)

Compiler: Compiled 3304 to 2337 computations (29.3% saved)

bsearch50.0ms (0.5%)

Steps

Iters	Range		Point
8	-3.412267100229742e-19	-3.814568852083155e-23	-3.3566486846414096e-19

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	322	78
1	322	78

end0.0ms (0%)

sample2.9s (30.6%)

Algorithm

1×

intervals

Results

840.0ms	1815×	body	1024	valid
348.0ms	1372×	body	512	valid
301.0ms	310×	body	2048	valid
300.0ms	3748×	body	128	valid
114.0ms	755×	body	256	valid
78.0ms	1565×	body	128	nan
55.0ms	199×	body	1024	nan
50.0ms	837×	body	128	overflowed
44.0ms	241×	body	512	nan
19.0ms	151×	body	256	nan
1.0ms	23×	body	128	invalid
0.0ms	2×	body	512	invalid

Compiler

Compiled 522 to 365 computations (30.1% saved)

Details

analyze1.1s (11.9%)

sample72.0ms (0.8%)

simplify511.0ms (5.4%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite39.0ms (0.4%)

series623.0ms (6.6%)

simplify78.0ms (0.8%)

prune358.0ms (3.8%)

localize10.0ms (0.1%)

rewrite29.0ms (0.3%)

series627.0ms (6.7%)

simplify128.0ms (1.4%)

prune125.0ms (1.3%)

localize20.0ms (0.2%)

rewrite34.0ms (0.4%)

series1.3s (13.9%)

simplify68.0ms (0.7%)

prune211.0ms (2.2%)

localize14.0ms (0.1%)

rewrite36.0ms (0.4%)

series522.0ms (5.5%)

simplify135.0ms (1.4%)

prune102.0ms (1.1%)

regimes286.0ms (3%)

bsearch50.0ms (0.5%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample2.9s (30.6%)

Profiling