Details

analyze516.0ms (9.1%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample38.0ms (0.7%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
2.0ms	26×	body	128	nan
1.0ms	16×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify453.0ms (8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (363.0ms)

Iter	Nodes	Cost
0	4219	54
1	4219	54

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

18.8b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
0.9b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_100`
11×	`*-un-lft-identity_binary64_78`
8×	`add-log-exp_binary64_117`
7×	`sqrt-prod_binary64_94` `add-cube-cbrt_binary64_113`
6×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `sqrt-div_binary64_95`
3×	`flip3--_binary64_82` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `difference-of-squares_binary64_47` `pow1/2_binary64_158`
1×	`+-commutative_binary64_8` `flip-+_binary64_52` `distribute-lft-out--_binary64_30` `diff-log_binary64_170` `distribute-lft-out_binary64_29` `sub-neg_binary64_71` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 59

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series232.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
58.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
57.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify95.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4936	1457
1	4936	1457

prune153.0ms (2.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Error

6.6b

Counts

72 → 11

Compiler

Compiled 3485 to 2117 computations (39.3% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

10.7b	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_100`
9×	`sqrt-prod_binary64_94`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
6×	`add-log-exp_binary64_117` `sqrt-div_binary64_95`
4×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
3×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `flip3--_binary64_82` `flip--_binary64_53` `pow1/2_binary64_158`
1×	`+-commutative_binary64_8` `flip-+_binary64_52` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 56

Calls

4 calls:

4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))

series229.0ms (4%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
55.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
54.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify112.0ms (2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4930	1361
1	4930	1361

prune156.0ms (2.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	68	11	79

Error

6.6b

Counts

79 → 11

Compiler

Compiled 4059 to 2476 computations (39% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

8.5b	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`add-log-exp_binary64_117` `cbrt-prod_binary64_109`
5×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `cbrt-div_binary64_110` `add-exp-log_binary64_116`
3×	`sqrt-prod_binary64_94` `flip3--_binary64_82` `flip--_binary64_53`
2×	`pow1/3_binary64_160` `sqrt-div_binary64_95`
1×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))

series360.0ms (6.3%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
98.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
90.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
53.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4964	1672
1	4964	1672

prune157.0ms (2.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	64	11	75

Error

6.6b

Counts

75 → 11

Compiler

Compiled 4018 to 2474 computations (38.4% saved)

localize33.0ms (0.6%)

Local error

Found 4 expressions with local error:

20.8b	(+.f64 b (.f64 (fabs.f64 (exp.f64 (log.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
22.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
23.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`add-log-exp_binary64_117` `cbrt-prod_binary64_109`
5×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `cbrt-div_binary64_110` `add-exp-log_binary64_116`
3×	`sqrt-prod_binary64_94` `flip3--_binary64_82` `flip--_binary64_53`
2×	`pow1/3_binary64_160` `sqrt-div_binary64_95`
1×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 52

Calls

4 calls:

4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(+.f64 b (.f64 (fabs.f64 (exp.f64 (log.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))

series356.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

121.0ms	(+.f64 b (.f64 (fabs.f64 (exp.f64 (log.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
95.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
83.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify54.0ms (1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4920	1672
1	4920	1672

prune150.0ms (2.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	64	11	75

Error

6.6b

Counts

75 → 11

Compiler

Compiled 3724 to 2298 computations (38.3% saved)

regimes434.0ms (7.6%)

Accuracy

Total 1.2b remaining (13.4%)

Threshold costs 0b (0%)

Compiler

Compiled 4914 to 3394 computations (30.9% saved)

bsearch61.0ms (1.1%)

Steps

Iters	Range		Point
7	2.1770504301334278e+47	5.6409200446738983e+48	5.586819839771134e+48
5	-3.240249624041544e+157	-1.3484075712682967e+157	-1.36144842074905e+157

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	163	172
1	163	172

end0.0ms (0%)

sample1.9s (32.9%)

Algorithm

1×

intervals

Results

706.0ms	8000×	body	128	valid
50.0ms	622×	body	128	nan
32.0ms	387×	body	128	invalid

Compiler

Compiled 1362 to 933 computations (31.5% saved)

Details

analyze516.0ms (9.1%)

sample38.0ms (0.7%)

simplify453.0ms (8%)

prune5.0ms (0.1%)

localize25.0ms (0.4%)

rewrite25.0ms (0.4%)

series232.0ms (4.1%)

simplify95.0ms (1.7%)

prune153.0ms (2.7%)

localize24.0ms (0.4%)

rewrite18.0ms (0.3%)

series229.0ms (4%)

simplify112.0ms (2%)

prune156.0ms (2.7%)

localize27.0ms (0.5%)

rewrite17.0ms (0.3%)

series360.0ms (6.3%)

simplify74.0ms (1.3%)

prune157.0ms (2.8%)

localize33.0ms (0.6%)

rewrite18.0ms (0.3%)

series356.0ms (6.2%)

simplify54.0ms (1%)

prune150.0ms (2.6%)

regimes434.0ms (7.6%)

bsearch61.0ms (1.1%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.9s (32.9%)

Profiling