Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample93.0ms (1.9%)

Algorithm

1×

intervals

Results

69.0ms	139×	body	2048	valid
14.0ms	67×	body	1024	valid
3.0ms	29×	body	512	valid
1.0ms	14×	body	128	valid
0.0ms	7×	body	256	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify186.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4809	13
1	4809	13

prune2.0ms (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

Error

27.7b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2)
4.0b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_1442`
9×	`add-log-exp_binary64_1481`
6×	`cancel-sign-sub-inv_binary64_1408` `add-sqr-sqrt_binary64_1464`
4×	`associate-+l+_binary64_1375` `frac-add_binary64_1450` `add-cube-cbrt_binary64_1477`
3×	`flip3--_binary64_1446` `flip--_binary64_1417`
2×	`add-cbrt-cube_binary64_1478` `sum-log_binary64_1533` `sub-neg_binary64_1435` `add-exp-log_binary64_1480` `distribute-lft-out_binary64_1393` `diff-log_binary64_1534` `exp-diff_binary64_1490` `pow1_binary64_1503` `neg-sub0_binary64_1437` `distribute-lft-out--_binary64_1394` `exp-neg_binary64_1489`
1×	`+-commutative_binary64_1372` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-+l-_binary64_1377` `difference-of-squares_binary64_1411`

Counts

2 → 39

Calls

2 calls:

9.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
4.0ms	(-.f64 (exp.f64 x) 2)

series35.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

28.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
8.0ms	(-.f64 (exp.f64 x) 2)

simplify53.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4887	654
1	4887	654

prune49.0ms (1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	4	46

Error

0.0b

Counts

46 → 4

Compiler

Compiled 667 to 355 computations (46.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
0.0b	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
0.0b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1464`
14×	`associate-r_binary64_1382` `add-exp-log_binary64_1480`
11×	`add-log-exp_binary64_1481`
10×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`add-cbrt-cube_binary64_1478` `unpow-prod-down_binary64_1521`
6×	`associate-l_binary64_1383` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`
4×	`sum-log_binary64_1533` `sqr-pow_binary64_1414` `pow1_binary64_1503`
2×	`cbrt-unprod_binary64_1475` `pow-exp_binary64_1510` `+-commutative_binary64_1372` `*-commutative_binary64_1373` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow-to-exp_binary64_1511`
1×	`associate-+r+_binary64_1374`

Counts

4 → 74

Calls

4 calls:

8.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
7.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
6.0ms	(*.f64 1/12 (pow.f64 x 4))
6.0ms	(*.f64 1/360 (pow.f64 x 6))

series171.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
29.0ms	(*.f64 1/360 (pow.f64 x 6))
29.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
24.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify85.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5006	1259

prune103.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	84	6	90

Error

0.0b

Counts

90 → 6

Compiler

Compiled 1851 to 1302 computations (29.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))
2.7b	(exp.f64 (log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))))
31.3b	(log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_1464`
15×	`add-exp-log_binary64_1480`
14×	`associate-r_binary64_1382`
13×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`add-cbrt-cube_binary64_1478` `unpow-prod-down_binary64_1521`
6×	`log-prod_binary64_1528` `associate-l_binary64_1383` `prod-exp_binary64_1491` `pow1_binary64_1503` `unswap-sqr_binary64_1410`
4×	`add-log-exp_binary64_1481` `exp-prod_binary64_1494` `sqr-pow_binary64_1414` `log-div_binary64_1529`
3×	`exp-sum_binary64_1488`
2×	`cbrt-unprod_binary64_1475` `pow-exp_binary64_1510` `log-pow_binary64_1531` `*-commutative_binary64_1373` `exp-diff_binary64_1490` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow-to-exp_binary64_1511`
1×	`rem-exp-log_binary64_1482` `rem-log-exp_binary64_1483`

Counts

4 → 81

Calls

4 calls:

8.0ms	(exp.f64 (log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))))
7.0ms	(log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
6.0ms	(*.f64 1/360 (pow.f64 x 6))
6.0ms	(*.f64 1/12 (pow.f64 x 4))

series161.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(exp.f64 (log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6))))))
41.0ms	(log.f64 (+.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
30.0ms	(*.f64 1/360 (pow.f64 x 6))
25.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify59.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4982	1721
1	4982	1721

prune128.0ms (2.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	93	6	99

Error

0.0b

Counts

99 → 6

Compiler

Compiled 2295 to 1670 computations (27.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))
0.0b	(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))
0.0b	(pow.f64 (exp.f64 x) 3)
3.0b	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_1442`
12×	`add-sqr-sqrt_binary64_1464`
11×	`add-log-exp_binary64_1481`
10×	`add-cube-cbrt_binary64_1477`
7×	`add-cbrt-cube_binary64_1478` `pow1_binary64_1503`
5×	`add-exp-log_binary64_1480`
4×	`sum-log_binary64_1533` `pow-pow_binary64_1514`
3×	`associate-r_binary64_1382` `cube-prod_binary64_1470` `associate-l_binary64_1383` `pow-unpow_binary64_1519` `distribute-lft-out_binary64_1393` `exp-prod_binary64_1494` `flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-+r+_binary64_1374` `unpow-prod-down_binary64_1521`
2×	`associate-*r/_binary64_1384` `+-commutative_binary64_1372` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392`
1×	`cube-mult_binary64_1472` `cbrt-unprod_binary64_1475` `pow-exp_binary64_1510` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `rem-cube-cbrt_binary64_1465` `sqr-pow_binary64_1414` `unpow3_binary64_1508` `prod-exp_binary64_1491` `pow-to-exp_binary64_1511` `unswap-sqr_binary64_1410`

Counts

4 → 76

Calls

4 calls:

9.0ms	(+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))
7.0ms	(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))
4.0ms	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))))
4.0ms	(pow.f64 (exp.f64 x) 3)

series166.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(+.f64 4 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))))
45.0ms	(.f64 (exp.f64 x) (+.f64 4 (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 2))))
30.0ms	(+.f64 (exp.f64 x) (+.f64 -6 (pow.f64 (exp.f64 x) 3)))
20.0ms	(pow.f64 (exp.f64 x) 3)

simplify65.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5123	1524

prune119.0ms (2.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	88	6	94

Error

0.0b

Counts

94 → 6

Compiler

Compiled 2871 to 1668 computations (41.9% saved)

regimes60.0ms (1.2%)

Accuracy

Total 0.6b remaining (97.7%)

Threshold costs 0.6b (97.7%)

Compiler

Compiled 648 to 480 computations (25.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	22
1	17	22

end0.0ms (0%)

sample3.2s (65.1%)

Algorithm

1×

intervals

Results

2.1s	4146×	body	2048	valid
440.0ms	2022×	body	1024	valid
111.0ms	996×	body	512	valid
33.0ms	490×	body	256	valid
13.0ms	346×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 347 to 261 computations (24.8% saved)

Details

analyze4.0ms (0.1%)

sample93.0ms (1.9%)

simplify186.0ms (3.8%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite16.0ms (0.3%)

series35.0ms (0.7%)

simplify53.0ms (1.1%)

prune49.0ms (1%)

localize10.0ms (0.2%)

rewrite32.0ms (0.7%)

series171.0ms (3.5%)

simplify85.0ms (1.7%)

prune103.0ms (2.1%)

localize15.0ms (0.3%)

rewrite34.0ms (0.7%)

series161.0ms (3.3%)

simplify59.0ms (1.2%)

prune128.0ms (2.6%)

localize14.0ms (0.3%)

rewrite31.0ms (0.6%)

series166.0ms (3.4%)

simplify65.0ms (1.3%)

prune119.0ms (2.4%)

regimes60.0ms (1.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.2s (65.1%)

Profiling