Details

analyze160.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 7 to 7 computations (0% saved)

sample143.0ms (0.1%)

Algorithm

1×

intervals

Results

51.0ms	54×	body	2048	valid
31.0ms	59×	body	1024	valid
10.0ms	34×	body	512	valid
8.0ms	23×	body	256	valid
7.0ms	86×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify558.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (234.0ms)

Iter	Nodes	Cost
0	4875	9
1	4875	9

prune9.0ms (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: 31.2b

Counts

2 → 1

Compiler

Compiled 12 to 12 computations (0% saved)

localize16.0ms (0%)

Local error

Found 2 expressions with local error:

0.1b	(exp.f64 (*.f64 a x))
4.2b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite29.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64_1464`
6×	`add-log-exp_binary64_1481` `*-un-lft-identity_binary64_1442`
3×	`cancel-sign-sub-inv_binary64_1408` `add-cube-cbrt_binary64_1477`
2×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503` `difference-of-squares_binary64_1411`
1×	`sub-neg_binary64_1435` `rem-exp-log_binary64_1482` `flip3--_binary64_1446` `difference-of-sqr-1_binary64_1412` `exp-prod_binary64_1494` `flip--_binary64_1417` `diff-log_binary64_1534` `exp-to-pow_binary64_1504` `distribute-lft-out--_binary64_1394`

Counts

2 → 28

Calls

2 calls:

15.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
11.0ms	(exp.f64 (*.f64 a x))

series128.0ms (0%)

Counts

2 → 6

Calls

2 calls:

88.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
39.0ms	(exp.f64 (*.f64 a x))

simplify351.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (318.0ms)

Iter	Nodes	Cost
0	4961	377
1	4961	377

prune357.0ms (0.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	20	14	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	15	35

Merged error: 4.7b

Counts

35 → 15

Compiler

Compiled 537 to 299 computations (44.3% saved)

localize52.0ms (0%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
4.4b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
5.6b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
8.4b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite127.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_1480`
13×	`add-cbrt-cube_binary64_1478` `add-sqr-sqrt_binary64_1464`
10×	`pow1_binary64_1503`
9×	`associate-l_binary64_1383` `prod-exp_binary64_1491` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
7×	`associate-r_binary64_1382`
6×	`add-log-exp_binary64_1481`
5×	`cbrt-unprod_binary64_1475`
4×	`associate-*r/_binary64_1384`
3×	`pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `flip3-+_binary64_1445` `flip-+_binary64_1416`
2×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `unswap-sqr_binary64_1410`
1×	`sum-log_binary64_1533` `pow-exp_binary64_1510` `+-commutative_binary64_1372` `pow-to-exp_binary64_1511`

Counts

4 → 74

Calls

4 calls:

39.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
25.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
22.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
19.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))

series1.3s (0.5%)

Counts

4 → 12

Calls

4 calls:

496.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
406.0ms	(.f64 x (+.f64 a (.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3)))))))
211.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
155.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

simplify109.0ms (0%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5442	1832

prune1.9s (0.7%)

Pruning

50 alts after pruning (49 fresh and 1 done)

	Pruned	Kept	Total
New	50	36	86
Fresh	0	13	13
Picked	1	0	1
Done	0	1	1
Total	51	50	101

Merged error: 0.1b

Counts

101 → 50

Compiler

Compiled 3532 to 2218 computations (37.2% saved)

localize73.0ms (0%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.7b	(.f64 x (+.f64 a (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))) (cbrt.f64 x)))))
2.0b	(.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))) (cbrt.f64 x))
2.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))) (cbrt.f64 x)))

rewrite250.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-exp-log_binary64_1480` `pow1_binary64_1503`
31×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491`
30×	`add-cbrt-cube_binary64_1478`
11×	`add-sqr-sqrt_binary64_1464`
10×	`associate-r_binary64_1382`
9×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`associate-*r/_binary64_1384`
6×	`cbrt-prod_binary64_1473`
5×	`associate-l_binary64_1383`
4×	`add-log-exp_binary64_1481` `associate-*l/_binary64_1385`
3×	`*-commutative_binary64_1373` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `pow1/3_binary64_1524` `unswap-sqr_binary64_1410`

Counts

4 → 95

Calls

4 calls:

81.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))) (cbrt.f64 x)))
80.0ms	(.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))) (cbrt.f64 x))
32.0ms	(.f64 x (+.f64 a (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))) (cbrt.f64 x)))))
11.0ms	(cbrt.f64 x)

series2.1s (0.8%)

Counts

4 → 12

Calls

4 calls:

611.0ms	(.f64 x (+.f64 a (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (.f64 x 1/6) a))) (cbrt.f64 x)))))
579.0ms	(.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))) (cbrt.f64 x))
484.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (.f64 a a) (+.f64 1/2 (.f64 (*.f64 x 1/6) a))) (cbrt.f64 x)))
408.0ms	(cbrt.f64 x)

simplify289.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (197.0ms)

Iter	Nodes	Cost
0	4983	2315
1	4983	2315

prune4.4s (1.7%)

Pruning

74 alts after pruning (73 fresh and 1 done)

	Pruned	Kept	Total
New	74	33	107
Fresh	8	40	48
Picked	1	0	1
Done	0	1	1
Total	83	74	157

Merged error: 0.1b

Counts

157 → 74

Compiler

Compiled 5081 to 2968 computations (41.6% saved)

localize121.0ms (0%)

Local error

Found 4 expressions with local error:

2.6b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6)))))) (cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6))))))) (cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6))))))))
27.9b	(cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6))))))
27.9b	(cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6))))))
27.9b	(cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6))))))

rewrite382.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

154×	`associate-*r/_binary64_1384`
60×	`cbrt-div_binary64_1474`
30×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
28×	`frac-times_binary64_1452`
25×	`add-exp-log_binary64_1480` `pow1_binary64_1503`
19×	`pow-prod-down_binary64_1513`
15×	`cbrt-unprod_binary64_1475` `prod-exp_binary64_1491`
14×	`associate-*l/_binary64_1385`
11×	`add-cbrt-cube_binary64_1478`
8×	`pow1/3_binary64_1524`
4×	`add-log-exp_binary64_1481` `add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
3×	`cbrt-prod_binary64_1473`
1×	`associate-r_binary64_1382` `associate-l_binary64_1383` `*-commutative_binary64_1373`

Counts

4 → 88

Calls

4 calls:

140.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6)))))) (cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6))))))) (cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6))))))))
50.0ms	(cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6))))))
50.0ms	(cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6))))))
39.0ms	(cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6))))))

series4.3s (1.7%)

Counts

4 → 12

Calls

4 calls:

1.3s	(cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6))))))
1.3s	(cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6))))))
1.3s	(cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6))))))
487.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6)))))) (cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6))))))) (cbrt.f64 (.f64 (cbrt.f64 x) (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6))))))))

simplify330.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	4959	4605
1	4959	4605

prune7.3s (2.8%)

Pruning

101 alts after pruning (99 fresh and 2 done)

	Pruned	Kept	Total
New	71	29	100
Fresh	2	70	72
Picked	0	1	1
Done	0	1	1
Total	73	101	174

Merged error: 0.1b

Counts

174 → 101

Compiler

Compiled 6282 to 3611 computations (42.5% saved)

regimes18.1s (7%)

Compiler: Compiled 41217 to 27471 computations (33.4% saved)

bsearch3.0min (70.4%)

Compiler: Compiled 3 to 3 computations (0% saved)

simplify54.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	89	226
1	89	226

end0.0ms (0%)

sample34.0s (13.1%)

Algorithm

1×

intervals

Results

1.4s	1483×	body	2048	valid
783.0ms	1710×	body	1024	valid
382.0ms	1152×	body	512	valid
290.0ms	3032×	body	128	valid
118.0ms	623×	body	256	valid
7.0ms	146×	body	128	invalid

Compiler

Compiled 9317 to 6137 computations (34.1% saved)

Pareto

0.7643036438123506

Details

analyze160.0ms (0.1%)

sample143.0ms (0.1%)

simplify558.0ms (0.2%)

prune9.0ms (0%)

localize16.0ms (0%)

rewrite29.0ms (0%)

series128.0ms (0%)

simplify351.0ms (0.1%)

prune357.0ms (0.1%)

localize52.0ms (0%)

rewrite127.0ms (0%)

series1.3s (0.5%)

simplify109.0ms (0%)

prune1.9s (0.7%)

localize73.0ms (0%)

rewrite250.0ms (0.1%)

series2.1s (0.8%)

simplify289.0ms (0.1%)

prune4.4s (1.7%)

localize121.0ms (0%)

rewrite382.0ms (0.1%)

series4.3s (1.7%)

simplify330.0ms (0.1%)

prune7.3s (2.8%)

regimes18.1s (7%)

bsearch3.0min (70.4%)

simplify54.0ms (0%)

end0.0ms (0%)

sample34.0s (13.1%)

Profiling