Details

analyze2.8s (16.6%)

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)

sample257.0ms (1.5%)

Algorithm

1×

intervals

Results

142.0ms	133×	body	2048	valid
45.0ms	71×	body	1024	valid
13.0ms	32×	body	1024	overflowed
10.0ms	16×	body	2048	overflowed
10.0ms	331×	pre	128	true
8.0ms	22×	body	512	valid
3.0ms	12×	body	512	overflowed
3.0ms	12×	body	256	valid
2.0ms	18×	body	128	valid
1.0ms	5×	body	256	overflowed
1.0ms	10×	body	128	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify198.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5217	37

prune10.0ms (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

60.0b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.5b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
4.7b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
5.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite70.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_1123`
26×	`*-un-lft-identity_binary64_1101`
15×	`cancel-sign-sub-inv_binary64_1067`
11×	`add-cube-cbrt_binary64_1136`
10×	`difference-of-squares_binary64_1070` `add-log-exp_binary64_1140`
9×	`flip--_binary64_1076` `flip3--_binary64_1105`
7×	`associate-r_binary64_1041` `associate-l_binary64_1042`
6×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
5×	`sub-neg_binary64_1094` `difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053`
4×	`frac-times_binary64_1111` `distribute-lft-in_binary64_1050` `distribute-rgt-in_binary64_1051`
3×	`diff-log_binary64_1193`
2×	`associate-r/_binary64_1043` `associate-l/_binary64_1044`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069`

Counts

4 → 96

Calls

4 calls:

24.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
10.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
9.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
9.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

series180.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

62.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
56.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
34.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
27.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

simplify148.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4967	2058
1	4967	2058

prune219.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	4	109

Error

50.1b

Counts

109 → 4

Compiler

Compiled 3462 to 1435 computations (58.5% saved)

localize55.0ms (0.3%)

Local error

Found 4 expressions with local error:

5.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
7.1b	(.f64 eps (.f64 1/6 (pow.f64 a 3)))
7.7b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3))))
13.6b	(.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))

rewrite75.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64_1139`
14×	`add-cbrt-cube_binary64_1137`
12×	`add-sqr-sqrt_binary64_1123`
11×	`pow1_binary64_1162`
10×	`*-un-lft-identity_binary64_1101` `prod-exp_binary64_1150`
8×	`add-log-exp_binary64_1140`
7×	`add-cube-cbrt_binary64_1136`
6×	`cbrt-unprod_binary64_1134`
4×	`associate-r_binary64_1041` `pow-prod-down_binary64_1172` `associate-l_binary64_1042`
3×	`cancel-sign-sub-inv_binary64_1067`
2×	`-commutative_binary64_1032` `difference-of-squares_binary64_1070` `flip3-+_binary64_1104` `associate-r/_binary64_1043` `flip-+_binary64_1075`
1×	`diff-log_binary64_1193` `pow-exp_binary64_1169` `sum-log_binary64_1192` `sub-neg_binary64_1094` `difference-of-sqr-1_binary64_1071` `distribute-lft-in_binary64_1050` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `+-commutative_binary64_1031` `unswap-sqr_binary64_1069` `pow-to-exp_binary64_1170` `distribute-rgt-in_binary64_1051`

Counts

4 → 71

Calls

4 calls:

22.0ms	(.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))
14.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3))))
12.0ms	(.f64 eps (.f64 1/6 (pow.f64 a 3)))
9.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series336.0ms (2%)

Counts

4 → 12

Calls

4 calls:

150.0ms	(.f64 (.f64 eps eps) (+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3)))))
83.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
55.0ms	(.f64 eps (.f64 1/6 (pow.f64 a 3)))
48.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 eps (.f64 1/6 (pow.f64 a 3))))

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5421	1533

prune189.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Error

48.5b

Counts

87 → 4

Compiler

Compiled 3818 to 1801 computations (52.8% saved)

localize42.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.2b	(pow.f64 (exp.f64 (.f64 eps eps)) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 eps 1/6) a))))
2.5b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
2.9b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 a eps) (log.f64 (pow.f64 (exp.f64 (.f64 eps eps)) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 eps 1/6) a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
5.1b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite62.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
15×	`add-sqr-sqrt_binary64_1123`
13×	`*-un-lft-identity_binary64_1101`
9×	`add-log-exp_binary64_1140`
8×	`associate-/r/_binary64_1047`
7×	`add-cube-cbrt_binary64_1136`
6×	`flip--_binary64_1076` `flip3--_binary64_1105` `cancel-sign-sub-inv_binary64_1067`
5×	`pow1_binary64_1162`
4×	`cbrt-unprod_binary64_1134` `difference-of-squares_binary64_1070` `frac-times_binary64_1111` `prod-exp_binary64_1150` `associate-*r/_binary64_1043` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
3×	`unpow-prod-down_binary64_1180` `pow-pow_binary64_1173` `flip3-+_binary64_1104` `flip-+_binary64_1075`
2×	`diff-log_binary64_1193` `sub-neg_binary64_1094` `unpow-prod-up_binary64_1179` `difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053` `associate-/l/_binary64_1048` `associate-*l/_binary64_1044`
1×	`pow-exp_binary64_1169` `frac-2neg_binary64_1112` `distribute-lft-in_binary64_1050` `clear-num_binary64_1100` `exp-prod_binary64_1153` `pow-unpow_binary64_1178` `div-inv_binary64_1098` `associate-/l_binary64_1046` `times-frac_binary64_1107` `sqr-pow_binary64_1073` `pow-to-exp_binary64_1170` `distribute-rgt-in_binary64_1051` `associate-/r_binary64_1045` `exp-to-pow_binary64_1163`

Counts

4 → 86

Calls

4 calls:

16.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 a eps) (log.f64 (pow.f64 (exp.f64 (.f64 eps eps)) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 eps 1/6) a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
8.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
7.0ms	(pow.f64 (exp.f64 (.f64 eps eps)) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 eps 1/6) a))))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series2.8s (16.4%)

Counts

4 → 12

Calls

4 calls:

2.6s	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (+.f64 (.f64 a eps) (log.f64 (pow.f64 (exp.f64 (.f64 eps eps)) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 eps 1/6) a)))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
77.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
53.0ms	(pow.f64 (exp.f64 (.f64 eps eps)) (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 eps 1/6) a))))
33.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

simplify158.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4998	3445
1	4998	3445

prune268.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	98	4	102

Error

0.1b

Counts

102 → 4

Compiler

Compiled 4915 to 2219 computations (54.9% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1101`
7×	`distribute-lft-out_binary64_1052`
6×	`times-frac_binary64_1107`
4×	`div-inv_binary64_1098`
3×	`add-sqr-sqrt_binary64_1123` `add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136`
1×	`sum-log_binary64_1192` `add-exp-log_binary64_1139` `pow1_binary64_1162` `flip3-+_binary64_1104` `add-cbrt-cube_binary64_1137` `+-commutative_binary64_1031` `flip-+_binary64_1075` `frac-add_binary64_1109`

Counts

1 → 19

Calls

1 calls:

20.0ms

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

series10.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify112.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4871	287
1	4871	287

prune20.0ms (0.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	20	6	26

Error

0.1b

Counts

26 → 6

Compiler

Compiled 255 to 197 computations (22.7% saved)

regimes367.0ms (2.2%)

Accuracy

Total 0.3b remaining (81.8%)

Threshold costs 0.3b (81.8%)

Compiler

Compiled 3982 to 2880 computations (27.7% saved)

bsearch5.0ms (0%)

Compiler: Compiled 24 to 19 computations (20.8% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	148
1	56	148

end0.0ms (0%)

sample8.5s (49.8%)

Algorithm

1×

intervals

Results

4.3s	4190×	body	2048	valid
1.2s	2350×	body	1024	valid
302.0ms	9675×	pre	128	true
260.0ms	602×	body	1024	overflowed
227.0ms	354×	body	2048	overflowed
219.0ms	688×	body	512	valid
76.0ms	278×	body	512	overflowed
50.0ms	512×	body	128	valid
47.0ms	249×	body	256	valid
30.0ms	147×	body	256	overflowed
29.0ms	292×	body	128	overflowed
17.0ms	11×	body	4096	valid
1.0ms	1×	body	2048	invalid
1.0ms	1×	body	4096	invalid

Compiler

Compiled 1115 to 792 computations (29% saved)

Details

analyze2.8s (16.6%)

sample257.0ms (1.5%)

simplify198.0ms (1.2%)

prune10.0ms (0.1%)

localize33.0ms (0.2%)

rewrite70.0ms (0.4%)

series180.0ms (1.1%)

simplify148.0ms (0.9%)

prune219.0ms (1.3%)

localize55.0ms (0.3%)

rewrite75.0ms (0.4%)

series336.0ms (2%)

simplify67.0ms (0.4%)

prune189.0ms (1.1%)

localize42.0ms (0.3%)

rewrite62.0ms (0.4%)

series2.8s (16.4%)

simplify158.0ms (0.9%)

prune268.0ms (1.6%)

localize6.0ms (0%)

rewrite21.0ms (0.1%)

series10.0ms (0.1%)

simplify112.0ms (0.7%)

prune20.0ms (0.1%)

regimes367.0ms (2.2%)

bsearch5.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample8.5s (49.8%)

Profiling