Details

analyze461.0ms (8.7%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample36.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	183×	body	128	valid
8.0ms	33×	body	2048	valid
4.0ms	19×	body	1024	valid
2.0ms	8×	body	4096	valid
1.0ms	7×	body	512	valid
1.0ms	13×	body	128	nan
1.0ms	14×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify427.0ms (8.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (329.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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

31.2b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1101`
15×	`add-sqr-sqrt_binary64_1123`
14×	`add-cube-cbrt_binary64_1136`
12×	`times-frac_binary64_1107`
8×	`add-log-exp_binary64_1140`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
5×	`distribute-lft-out_binary64_1052` `pow1_binary64_1162`
4×	`associate-/l*_binary64_1046`
3×	`sqrt-prod_binary64_1117` `associate-/r*_binary64_1045`
2×	`flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate-/l/_binary64_1048` `sqrt-div_binary64_1118` `flip-+_binary64_1075`
1×	`diff-log_binary64_1193` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `sub-neg_binary64_1094` `sqrt-pow1_binary64_1119` `clear-num_binary64_1100` `div-inv_binary64_1098` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cancel-sign-sub-inv_binary64_1067` `pow1/2_binary64_1181`

Counts

4 → 72

Calls

4 calls:

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

series241.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
70.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
64.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
33.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify92.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4970	2025
1	4970	2025

prune118.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	8	85

Error

5.9b

Counts

85 → 8

Compiler

Compiled 2141 to 1155 computations (46.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
7.8b	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
23.0b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
23.0b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_1140`
6×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136` `cbrt-prod_binary64_1132`
4×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137` `cbrt-div_binary64_1133`
3×	`flip--_binary64_1076` `flip3--_binary64_1105`
2×	`pow1/3_binary64_1183`
1×	`diff-log_binary64_1193` `sum-log_binary64_1192` `sub-neg_binary64_1094` `flip3-+_binary64_1104` `+-commutative_binary64_1031` `flip-+_binary64_1075` `cancel-sign-sub-inv_binary64_1067`

Counts

4 → 49

Calls

4 calls:

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

series330.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
91.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
86.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
33.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify54.0ms (1%)

Algorithm

1×	egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4977	1572
1	4977	1572

prune96.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	61	8	69

Error

5.9b

Counts

69 → 8

Compiler

Compiled 2325 to 1303 computations (44% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
2.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1101`
8×	`add-sqr-sqrt_binary64_1123` `add-log-exp_binary64_1140`
6×	`pow1_binary64_1162` `sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136`
4×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118`
2×	`rem-sqrt-square_binary64_1114` `distribute-lft-out_binary64_1052` `sum-log_binary64_1192` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `+-commutative_binary64_1031` `flip-+_binary64_1075` `pow1/2_binary64_1181`

Counts

4 → 54

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series237.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
57.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
55.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5082	1354

prune99.0ms (1.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	66	8	74

Error

5.9b

Counts

74 → 8

Compiler

Compiled 2536 to 1377 computations (45.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
2.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
22.2b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1101`
8×	`add-sqr-sqrt_binary64_1123` `add-log-exp_binary64_1140`
6×	`pow1_binary64_1162` `sqrt-prod_binary64_1117` `add-cube-cbrt_binary64_1136`
4×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `sqrt-div_binary64_1118`
2×	`rem-sqrt-square_binary64_1114` `distribute-lft-out_binary64_1052` `sum-log_binary64_1192` `sqrt-pow1_binary64_1119` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `+-commutative_binary64_1031` `flip-+_binary64_1075` `pow1/2_binary64_1181`

Counts

4 → 54

Calls

4 calls:

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

series237.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
59.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
56.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

simplify65.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5082	1354

prune95.0ms (1.8%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	66	8	74

Error

5.9b

Counts

74 → 8

Compiler

Compiled 2450 to 1310 computations (46.5% saved)

regimes532.0ms (10%)

Accuracy

Total 3.4b remaining (37%)

Threshold costs 0b (0%)

Compiler

Compiled 3004 to 2222 computations (26% saved)

bsearch106.0ms (2%)

Steps

Iters	Range	Point
8	1.4321713852773844e+135	2.1090845602311984e+139	1.6833943237704546e+136
9	-1.8898449676445546e-99	-2.875154670333836e-106	-2.058574872602062e-105
8	-1.7915129492577403e+88	-1.3262247074219856e+85	-2.6479930097769547e+85

Iters

Range

Point

1.4321713852773844e+135

2.1090845602311984e+139

1.6833943237704546e+136

-1.8898449676445546e-99

-2.875154670333836e-106

-2.058574872602062e-105

-1.7915129492577403e+88

-1.3262247074219856e+85

-2.6479930097769547e+85

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	127	103
1	127	103

end0.0ms (0%)

sample1.8s (34.8%)

Algorithm

1×

intervals

Results

285.0ms	1143×	body	2048	valid
273.0ms	5236×	body	128	valid
135.0ms	686×	body	1024	valid
115.0ms	385×	body	4096	valid
56.0ms	374×	body	512	valid
30.0ms	619×	body	128	nan
20.0ms	392×	body	128	invalid
19.0ms	176×	body	256	valid

Compiler

Compiled 870 to 634 computations (27.1% saved)

Details

analyze461.0ms (8.7%)

sample36.0ms (0.7%)

simplify427.0ms (8.1%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite29.0ms (0.5%)

series241.0ms (4.5%)

simplify92.0ms (1.7%)

prune118.0ms (2.2%)

localize15.0ms (0.3%)

rewrite21.0ms (0.4%)

series330.0ms (6.2%)

simplify54.0ms (1%)

prune96.0ms (1.8%)

localize13.0ms (0.3%)

rewrite26.0ms (0.5%)

series237.0ms (4.5%)

simplify63.0ms (1.2%)

prune99.0ms (1.9%)

localize14.0ms (0.3%)

rewrite27.0ms (0.5%)

series237.0ms (4.5%)

simplify65.0ms (1.2%)

prune95.0ms (1.8%)

regimes532.0ms (10%)

bsearch106.0ms (2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.8s (34.8%)

Profiling