Details

analyze489.0ms (8.4%)

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)

sample33.0ms (0.6%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
1.0ms	16×	body	128	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify252.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	1224	54
1	1224	54

prune9.0ms (0.2%)

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

Merged error: 23.4b

Counts

2 → 1

Compiler

Compiled 146 to 101 computations (30.8% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_101` `add-log-exp_binary64_118`
6×	`sqrt-prod_binary64_95` `add-cube-cbrt_binary64_114` `pow1_binary64_140` `*-un-lft-identity_binary64_79`
4×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `flip--_binary64_54` `sqrt-div_binary64_96` `flip3--_binary64_83`
2×	`rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `diff-log_binary64_171` `pow1/2_binary64_159` `cancel-sign-sub-inv_binary64_45` `sub-neg_binary64_72`

Counts

4 → 54

Calls

4 calls:

6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series363.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5365	1236

prune248.0ms (4.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	60	6	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	7	67

Merged error: 9.7b

Counts

67 → 7

Compiler

Compiled 5778 to 3729 computations (35.5% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

8.6b	(+.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))))))
25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.4b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.4b	(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_101`
7×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
6×	`add-log-exp_binary64_118` `cbrt-prod_binary64_110`
5×	`pow1_binary64_140`
4×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `cbrt-div_binary64_111`
3×	`sqrt-prod_binary64_95` `flip--_binary64_54` `flip3--_binary64_83`
2×	`sqrt-div_binary64_96` `pow1/3_binary64_161`
1×	`flip-+_binary64_53` `sum-log_binary64_170` `+-commutative_binary64_9` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `pow1/2_binary64_159` `flip3-+_binary64_82`

Counts

4 → 52

Calls

4 calls:

5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(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 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))

series668.0ms (11.4%)

Counts

4 → 12

Calls

4 calls:

201.0ms	(+.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))))))
177.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
168.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify58.0ms (1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4959	1672
1	4959	1672

prune233.0ms (4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	62	9	71

Merged error: 9.7b

Counts

71 → 9

Compiler

Compiled 5740 to 3644 computations (36.5% saved)

localize32.0ms (0.6%)

Local error

Found 4 expressions with local error:

25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.4b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_101`
9×	`sqrt-prod_binary64_95`
8×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
7×	`pow1_binary64_140`
6×	`sqrt-div_binary64_96`
4×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `flip--_binary64_54` `add-log-exp_binary64_118` `flip3--_binary64_83`
3×	`rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `cbrt-prod_binary64_110` `pow1/2_binary64_159`
2×	`cbrt-div_binary64_111`
1×	`pow1/3_binary64_161`

Counts

4 → 58

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series524.0ms (9%)

Counts

4 → 12

Calls

4 calls:

164.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4854	1408
1	4854	1408

prune198.0ms (3.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	70	9	79

Merged error: 9.7b

Counts

79 → 9

Compiler

Compiled 5100 to 3110 computations (39% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
26.4b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_101`
9×	`sqrt-prod_binary64_95`
8×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
7×	`pow1_binary64_140`
6×	`sqrt-div_binary64_96`
4×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `flip--_binary64_54` `add-log-exp_binary64_118` `flip3--_binary64_83`
3×	`rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `cbrt-prod_binary64_110` `pow1/2_binary64_159`
2×	`cbrt-div_binary64_111`
1×	`pow1/3_binary64_161`

Counts

4 → 58

Calls

4 calls:

7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series547.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
127.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify78.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4854	1408
1	4854	1408

prune202.0ms (3.5%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	70	9	79

Merged error: 9.7b

Counts

79 → 9

Compiler

Compiled 4809 to 2909 computations (39.5% saved)

regimes160.0ms (2.7%)

Compiler: Compiled 1320 to 918 computations (30.5% saved)

bsearch85.0ms (1.5%)

Steps

Iters	Range		Point
9	2.7667221834522944e+79	6.980360605296595e+84	3.148606068148581e+83
9	-7.769097205397194e+154	-3.112609503432856e+149	-1.3610757459905584e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	137	170
1	137	170

end0.0ms (0%)

sample1.4s (23.2%)

Algorithm

1×

intervals

Results

672.0ms	8000×	body	128	valid
56.0ms	724×	body	128	nan
30.0ms	380×	body	128	invalid

Compiler

Compiled 591 to 401 computations (32.1% saved)

Details

analyze489.0ms (8.4%)

sample33.0ms (0.6%)

simplify252.0ms (4.3%)

prune9.0ms (0.2%)

localize21.0ms (0.4%)

rewrite22.0ms (0.4%)

series363.0ms (6.2%)

simplify57.0ms (1%)

prune248.0ms (4.2%)

localize27.0ms (0.5%)

rewrite18.0ms (0.3%)

series668.0ms (11.4%)

simplify58.0ms (1%)

prune233.0ms (4%)

localize32.0ms (0.6%)

rewrite21.0ms (0.4%)

series524.0ms (9%)

simplify76.0ms (1.3%)

prune198.0ms (3.4%)

localize29.0ms (0.5%)

rewrite24.0ms (0.4%)

series547.0ms (9.4%)

simplify78.0ms (1.3%)

prune202.0ms (3.5%)

regimes160.0ms (2.7%)

bsearch85.0ms (1.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (23.2%)

Profiling