Details

analyze760.0ms (15.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample50.0ms (1%)

Algorithm

1×

intervals

Results

23.0ms	87×	body	1024	valid
5.0ms	36×	body	512	valid
5.0ms	15×	body	2048	valid
5.0ms	103×	body	128	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

prune3.0ms (0.1%)

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

Error

40.9b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.5b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.2b	(-.f64 (exp.f64 x) 1)

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_1464`
30×	`*-un-lft-identity_binary64_1442`
21×	`times-frac_binary64_1448`
15×	`add-cube-cbrt_binary64_1477`
10×	`difference-of-squares_binary64_1411`
7×	`associate-/r*_binary64_1386`
5×	`difference-of-sqr-1_binary64_1412` `distribute-lft-out--_binary64_1394`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481`
3×	`cancel-sign-sub-inv_binary64_1408` `associate-/l*_binary64_1387` `add-exp-log_binary64_1480`
2×	`associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417` `pow1_binary64_1503`
1×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `div-exp_binary64_1493`

Counts

2 → 63

Calls

2 calls:

13.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
9.0ms	(-.f64 (exp.f64 x) 1)

series114.0ms (2.3%)

Counts

2 → 12

Calls

2 calls:

83.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
30.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 140 to 111 computations (20.7% saved)

simplify117.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5105	1195

prune133.0ms (2.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	4	76

Error

Counts

76 → 4

Compiler

Compiled 1025 to 518 computations (49.5% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))))
0.0b	(.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))
0.3b	(.f64 x (+.f64 1/6 (.f64 1/24 x)))
0.3b	(*.f64 1/24 x)

rewrite62.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_1464`
17×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
15×	`add-cbrt-cube_binary64_1478`
14×	`add-exp-log_binary64_1480`
13×	`pow1_binary64_1503`
9×	`associate-r_binary64_1382` `times-frac_binary64_1448`
7×	`associate-l_binary64_1383`
5×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491`
4×	`associate-*r/_binary64_1384` `add-log-exp_binary64_1481`
3×	`associate-/r_binary64_1386` `associate-/l_binary64_1387` `*-commutative_binary64_1373` `flip3-+_binary64_1445` `flip-+_binary64_1416` `unswap-sqr_binary64_1410`
2×	`associate-/r/_binary64_1388` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
1×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `div-exp_binary64_1493`

Counts

4 → 92

Calls

4 calls:

14.0ms	(.f64 x (+.f64 1/6 (.f64 1/24 x)))
14.0ms	(.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))
10.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))))
8.0ms	(*.f64 1/24 x)

series358.0ms (7.3%)

Counts

4 → 23

Calls

4 calls:

173.0ms	(.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))
94.0ms	(.f64 x (+.f64 1/6 (.f64 1/24 x)))
58.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 (.f64 x x) (+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 1/24 x)))))))
33.0ms	(*.f64 1/24 x)

Compiler

Compiled 566 to 442 computations (21.9% saved)

simplify109.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5001	2300

prune221.0ms (4.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	115	4	119

Error

Counts

119 → 4

Compiler

Compiled 2798 to 1687 computations (39.7% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1/2 (/.f64 1 x))
0.0b	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
0.3b	(*.f64 x 1/12)

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-log-exp_binary64_1481`
8×	`*-un-lft-identity_binary64_1442`
7×	`add-sqr-sqrt_binary64_1464`
5×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
4×	`sum-log_binary64_1533`
3×	`associate-r_binary64_1382` `associate-l_binary64_1383`
2×	`+-commutative_binary64_1372` `distribute-lft-out_binary64_1393` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`cbrt-unprod_binary64_1475` `associate-+l+_binary64_1375` `div-inv_binary64_1439` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`

Counts

3 → 44

Calls

3 calls:

16.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
11.0ms	(+.f64 1/2 (/.f64 1 x))
7.0ms	(*.f64 x 1/12)

series137.0ms (2.8%)

Counts

3 → 18

Calls

3 calls:

78.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
31.0ms	(*.f64 x 1/12)
28.0ms	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 203 to 184 computations (9.4% saved)

simplify147.0ms (3%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4880	618
1	4880	618

prune89.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	62	4	66

Error

Counts

66 → 4

Compiler

Compiled 755 to 604 computations (20% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
3.9b	(-.f64 1 (exp.f64 (neg.f64 x)))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
18×	`times-frac_binary64_1448`
14×	`add-cube-cbrt_binary64_1477`
10×	`difference-of-squares_binary64_1411`
6×	`associate-/r*_binary64_1386` `add-exp-log_binary64_1480`
5×	`distribute-lft-out--_binary64_1394`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481`
3×	`cancel-sign-sub-inv_binary64_1408` `associate-/l*_binary64_1387` `pow1_binary64_1503`
2×	`associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417` `div-exp_binary64_1493`
1×	`inv-pow_binary64_1527` `cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `1-exp_binary64_1486` `rec-exp_binary64_1492` `pow-flip_binary64_1516` `frac-2neg_binary64_1453` `diff-log_binary64_1534`

Counts

2 → 62

Calls

2 calls:

12.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
9.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

series115.0ms (2.3%)

Counts

2 → 12

Calls

2 calls:

78.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
36.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 140 to 131 computations (6.4% saved)

simplify146.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4951	1118
1	4951	1118

prune91.0ms (1.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	74	4	78

Error

Counts

78 → 4

Compiler

Compiled 917 to 587 computations (36% saved)

regimes150.0ms (3%)

Accuracy

Total 0.9b remaining (98.2%)

Threshold costs 0.9b (98.2%)

Compiler

Compiled 661 to 508 computations (23.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	27
1	20	27

end0.0ms (0%)

sample2.0s (39.9%)

Algorithm

1×

intervals

Results

703.0ms	2614×	body	1024	valid
200.0ms	1315×	body	512	valid
138.0ms	3158×	body	128	valid
88.0ms	285×	body	2048	valid
63.0ms	628×	body	256	valid

Compiler

Compiled 218 to 170 computations (22% saved)

Details

analyze760.0ms (15.4%)

sample50.0ms (1%)

simplify12.0ms (0.3%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

rewrite31.0ms (0.6%)

series114.0ms (2.3%)

simplify117.0ms (2.4%)

prune133.0ms (2.7%)

localize22.0ms (0.4%)

rewrite62.0ms (1.3%)

series358.0ms (7.3%)

simplify109.0ms (2.2%)

prune221.0ms (4.5%)

localize11.0ms (0.2%)

rewrite39.0ms (0.8%)

series137.0ms (2.8%)

simplify147.0ms (3%)

prune89.0ms (1.8%)

localize9.0ms (0.2%)

rewrite30.0ms (0.6%)

series115.0ms (2.3%)

simplify146.0ms (2.9%)

prune91.0ms (1.8%)

regimes150.0ms (3%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.0s (39.9%)

Profiling