Details

analyze1.8s (12.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

Compiler

Compiled 31 to 24 computations (22.6% saved)

sample220.0ms (1.5%)

Algorithm

1×

intervals

Results

146.0ms	161×	body	2048	valid
29.0ms	56×	body	1024	valid
7.0ms	312×	pre	128	true
6.0ms	18×	body	1024	overflowed
5.0ms	9×	body	2048	overflowed
5.0ms	17×	body	512	valid
3.0ms	11×	body	512	overflowed
1.0ms	17×	body	128	valid
1.0ms	8×	body	256	overflowed
1.0ms	1×	body	4096	valid
1.0ms	10×	body	128	overflowed
1.0ms	4×	body	256	valid

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify180.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5217	37

prune3.0ms (0%)

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: 60.1b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
1.5b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
2.9b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.8b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_1109`
21×	`*-un-lft-identity_binary64_1088`
10×	`add-log-exp_binary64_1124` `difference-of-squares_binary64_1057`
9×	`flip3--_binary64_1092` `flip--_binary64_1063`
7×	`associate-r_binary64_1030` `associate-l_binary64_1031`
6×	`add-cbrt-cube_binary64_1121` `add-exp-log_binary64_1123` `pow1_binary64_1146` `add-cube-cbrt_binary64_1120`
5×	`difference-of-sqr-1_binary64_1058` `sub-neg_binary64_1081` `distribute-lft-out--_binary64_1042`
4×	`frac-times_binary64_1098`
3×	`diff-log_binary64_1177`
2×	`associate-l/_binary64_1033` `associate-r/_binary64_1032`
1×	`*-commutative_binary64_1021` `unswap-sqr_binary64_1056` `cbrt-unprod_binary64_1118` `distribute-rgt-in_binary64_1040` `pow-prod-down_binary64_1156` `prod-exp_binary64_1134` `distribute-lft-in_binary64_1039`

Counts

4 → 81

Calls

4 calls:

12.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

series253.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

92.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
76.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
43.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
42.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5130	1893

prune127.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	3	94

Merged error: 52.5b

Counts

94 → 3

Compiler

Compiled 3032 to 1284 computations (57.7% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.3b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 a eps) (.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
5.8b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3))))
6.2b	(.f64 eps (.f64 1/6 (pow.f64 a 3)))
9.1b	(.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))

rewrite59.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64_1123`
26×	`add-cbrt-cube_binary64_1121`
14×	`prod-exp_binary64_1134`
11×	`pow1_binary64_1146`
10×	`cbrt-unprod_binary64_1118`
8×	`associate-/r/_binary64_1036`
7×	`add-sqr-sqrt_binary64_1109`
6×	`add-log-exp_binary64_1124` `-un-lft-identity_binary64_1088` `add-cube-cbrt_binary64_1120` `associate-r/_binary64_1032`
5×	`flip-+_binary64_1062` `flip3-+_binary64_1091`
4×	`associate-r_binary64_1030` `flip3--_binary64_1092` `frac-times_binary64_1098` `flip--_binary64_1063` `div-exp_binary64_1136` `associate-l_binary64_1031` `cbrt-undiv_binary64_1119` `pow-prod-down_binary64_1156`
2×	`-commutative_binary64_1021` `associate-l/_binary64_1033` `associate-/l/_binary64_1037`
1×	`clear-num_binary64_1087` `frac-2neg_binary64_1099` `unswap-sqr_binary64_1056` `distribute-rgt-in_binary64_1040` `associate-/r_binary64_1034` `sum-log_binary64_1176` `times-frac_binary64_1094` `pow-exp_binary64_1153` `+-commutative_binary64_1020` `pow-to-exp_binary64_1154` `associate-/l_binary64_1035` `distribute-lft-in_binary64_1039` `div-inv_binary64_1085`

Counts

4 → 84

Calls

4 calls:

17.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 a eps) (.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
13.0ms	(.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))
8.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3))))
7.0ms	(.f64 eps (.f64 1/6 (pow.f64 a 3)))

series3.8s (26.2%)

Counts

4 → 12

Calls

4 calls:

3.4s	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 a eps) (.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))) (-.f64 (exp.f64 (*.f64 b eps)) 1)))
191.0ms	(.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))
81.0ms	(.f64 eps (.f64 1/6 (pow.f64 a 3)))
81.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3))))

simplify82.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4993	3710
1	4993	3710

prune205.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	96	3	99

Merged error: 0.0b

Counts

99 → 3

Compiler

Compiled 4961 to 2469 computations (50.2% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1088`
7×	`distribute-lft-out_binary64_1041`
6×	`times-frac_binary64_1094`
4×	`div-inv_binary64_1085`
3×	`add-sqr-sqrt_binary64_1109` `add-log-exp_binary64_1124` `add-cube-cbrt_binary64_1120`
1×	`frac-add_binary64_1096` `add-cbrt-cube_binary64_1121` `sum-log_binary64_1176` `add-exp-log_binary64_1123` `+-commutative_binary64_1020` `flip-+_binary64_1062` `pow1_binary64_1146` `flip3-+_binary64_1091`

Counts

1 → 19

Calls

1 calls:

15.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

series21.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

21.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5088	287

prune24.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	20	5	25

Merged error: 0.0b

Counts

25 → 5

Compiler

Compiled 360 to 277 computations (23.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.5b	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))

rewrite109.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`*-un-lft-identity_binary64_1088`
114×	`cbrt-prod_binary64_1116`
81×	`distribute-lft-out_binary64_1041`
60×	`div-inv_binary64_1085`
42×	`times-frac_binary64_1094`
37×	`add-sqr-sqrt_binary64_1109`
33×	`swap-sqr_binary64_1055` `cbrt-div_binary64_1117`
29×	`add-cube-cbrt_binary64_1120`
13×	`associate-r_binary64_1030` `associate-l_binary64_1031`
11×	`frac-add_binary64_1096` `flip-+_binary64_1062` `pow1_binary64_1146` `flip3-+_binary64_1091`
9×	`frac-times_binary64_1098` `pow1/3_binary64_1167`
6×	`add-exp-log_binary64_1123`
4×	`add-cbrt-cube_binary64_1121` `unswap-sqr_binary64_1056` `add-log-exp_binary64_1124`
3×	`associate-l/_binary64_1033` `associate-r/_binary64_1032`
2×	`pow-prod-down_binary64_1156` `pow-sqr_binary64_1061` `pow-prod-up_binary64_1155`
1×	`*-commutative_binary64_1021` `pow-plus_binary64_1148` `cbrt-unprod_binary64_1118` `pow2_binary64_1166` `prod-exp_binary64_1134`

Counts

4 → 159

Calls

4 calls:

38.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
17.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
15.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
15.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

series606.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

184.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
143.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
141.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
138.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5290	4074

prune329.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	170	6	176

Merged error: 0.0b

Counts

176 → 6

Compiler

Compiled 5429 to 4235 computations (22% saved)

regimes56.0ms (0.4%)

Compiler: Compiled 483 to 402 computations (16.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	10
1	9	10

end0.0ms (0%)

sample6.3s (43.2%)

Algorithm

1×

intervals

Results

3.6s	4066×	body	2048	valid
1.1s	2403×	body	1024	valid
236.0ms	9690×	pre	128	true
210.0ms	599×	body	1024	overflowed
199.0ms	354×	body	2048	overflowed
197.0ms	734×	body	512	valid
66.0ms	288×	body	512	overflowed
46.0ms	274×	body	256	valid
41.0ms	513×	body	128	valid
23.0ms	300×	body	128	overflowed
22.0ms	148×	body	256	overflowed
15.0ms	10×	body	4096	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 204 to 169 computations (17.2% saved)

Details

analyze1.8s (12.5%)

sample220.0ms (1.5%)

simplify180.0ms (1.2%)

prune3.0ms (0%)

localize17.0ms (0.1%)

rewrite35.0ms (0.2%)

series253.0ms (1.7%)

simplify70.0ms (0.5%)

prune127.0ms (0.9%)

localize27.0ms (0.2%)

rewrite59.0ms (0.4%)

series3.8s (26.2%)

simplify82.0ms (0.6%)

prune205.0ms (1.4%)

localize5.0ms (0%)

rewrite16.0ms (0.1%)

series21.0ms (0.1%)

simplify85.0ms (0.6%)

prune24.0ms (0.2%)

localize9.0ms (0.1%)

rewrite109.0ms (0.8%)

series606.0ms (4.2%)

simplify69.0ms (0.5%)

prune329.0ms (2.3%)

regimes56.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.3s (43.2%)

Profiling