Details

analyze460.0ms (1.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	93.6%	6.4%	7
3.1%	84.2%	12.7%	8
12.5%	67.1%	20.5%	9
16%	63.5%	20.5%	10
17.9%	57.7%	24.4%	11
22.6%	48.7%	28.7%	12
28.7%	37.8%	33.6%	13
30.4%	35.9%	33.7%	14

Compiler

Compiled 9 to 9 computations (0% saved)

sample33.0ms (0.1%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
4.0ms	121×	body	128	nan
1.0ms	26×	body	128	invalid

Compiler

Compiled 17 to 21 computations (-23.5% saved)

simplify94.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	12
1	15	12

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

19.1b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

0.9b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
5.1b	(/.f64 A (*.f64 V l))
17.5b	(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite87.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

5.6b

Rules

16×	`add-sqr-sqrt_binary64_1123`
15×	`sqrt-prod_binary64_1117`
11×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
10×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `associate-r_binary64_1041`
9×	`times-frac_binary64_1107`
6×	`pow1_binary64_1162`
3×	`add-log-exp_binary64_1140` `div-inv_binary64_1098` `associate-/l_binary64_1046` `associate-l*_binary64_1042`
2×	`sqrt-div_binary64_1118` `prod-exp_binary64_1150` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cbrt-unprod_binary64_1134` `unswap-sqr_binary64_1069`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `rem-sqrt-square_binary64_1114` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/r_binary64_1045` `pow-prod-down_binary64_1172` `associate-r/_binary64_1043` `*-commutative_binary64_1032`

Counts

3 → 66

Calls

3 calls:

8.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
5.0ms	(/.f64 A (*.f64 V l))
4.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

Compiler

Compiled 937 to 244 computations (74% saved)

series324.0ms (1.2%)

Error

19.1b

Counts

3 → 30

Calls

3 calls:

140.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
109.0ms	(/.f64 A (*.f64 V l))
63.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

Compiler

Compiled 1032 to 758 computations (26.6% saved)

simplify77.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4894	1105
1	4894	1105

prune89.0ms (0.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	79	17	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	17	97

Error

5.6b

Counts

97 → 17

Compiler

Compiled 1307 to 409 computations (68.7% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

0.9b	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
2.7b	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
3.1b	(/.f64 V (/.f64 (cbrt.f64 A) l))
17.5b	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))

rewrite601.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

2.1b

Rules

849×	`times-frac_binary64_1107`
358×	`add-sqr-sqrt_binary64_1123`
331×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
157×	`sqrt-prod_binary64_1117`
146×	`cbrt-prod_binary64_1132`
93×	`associate-/r*_binary64_1045`
79×	`associate-r_binary64_1041`
32×	`add-exp-log_binary64_1139`
24×	`div-inv_binary64_1098`
23×	`add-cbrt-cube_binary64_1137`
15×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
8×	`associate-/r/_binary64_1047`
7×	`pow1_binary64_1162`
6×	`unswap-sqr_binary64_1069`
5×	`rem-sqrt-square_binary64_1114`
4×	`add-log-exp_binary64_1140` `associate-/l*_binary64_1046` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
3×	`associate-l_binary64_1042`
2×	`sqrt-div_binary64_1118` `frac-2neg_binary64_1112` `clear-num_binary64_1100`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `pow-prod-down_binary64_1172` `associate-r/_binary64_1043` `-commutative_binary64_1032`

Counts

4 → 463

Calls

4 calls:

32.0ms	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
19.0ms	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
18.0ms	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))
10.0ms	(/.f64 V (/.f64 (cbrt.f64 A) l))

Compiler

Compiled 12615 to 2772 computations (78% saved)

series739.0ms (2.8%)

Error

5.6b

Counts

4 → 39

Calls

4 calls:

335.0ms	(/.f64 V (/.f64 (cbrt.f64 A) l))
171.0ms	(.f64 c0 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))))
128.0ms	(/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l)))
81.0ms	(sqrt.f64 (/.f64 (*.f64 (cbrt.f64 A) (cbrt.f64 A)) (/.f64 V (/.f64 (cbrt.f64 A) l))))

Compiler

Compiled 1588 to 1179 computations (25.8% saved)

simplify170.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

502 → 502

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4992	12589
1	4992	12589

prune435.0ms (1.7%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	492	10	502
Fresh	7	9	16
Picked	1	0	1
Done	0	0	0
Total	500	19	519

Error

1.9b

Counts

519 → 19

Compiler

Compiled 12040 to 2273 computations (81.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 A)
1.4b	(.f64 (.f64 c0 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)))) (sqrt.f64 (/.f64 (cbrt.f64 A) (/.f64 (cbrt.f64 V) (/.f64 1 l)))))
1.4b	(/.f64 (cbrt.f64 A) (/.f64 (cbrt.f64 V) (/.f64 1 l)))
5.5b	(sqrt.f64 (/.f64 (cbrt.f64 A) (/.f64 (cbrt.f64 V) (/.f64 1 l))))

rewrite4.3s (16.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

4036×	`times-frac_binary64_1107`
1864×	`add-sqr-sqrt_binary64_1123`
1823×	`*-un-lft-identity_binary64_1101`
1819×	`add-cube-cbrt_binary64_1136`
1507×	`cbrt-prod_binary64_1132`
1006×	`sqrt-prod_binary64_1117`
506×	`associate-r_binary64_1041`
136×	`div-inv_binary64_1098`
83×	`associate-/r*_binary64_1045`
24×	`add-exp-log_binary64_1139`
22×	`associate-/r/_binary64_1047`
15×	`rem-sqrt-square_binary64_1114`
13×	`add-cbrt-cube_binary64_1137`
11×	`div-exp_binary64_1152`
10×	`pow1_binary64_1162`
6×	`cbrt-undiv_binary64_1135` `associate-/l*_binary64_1046`
4×	`add-log-exp_binary64_1140`
3×	`pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
2×	`sqrt-div_binary64_1118`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `1-exp_binary64_1145` `rec-exp_binary64_1151` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-r/_binary64_1043` `associate-l_binary64_1042` `-commutative_binary64_1032` `pow1/3_binary64_1183`

Counts

4 → 1667

Calls

4 calls:

121.0ms	(.f64 (.f64 c0 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)))) (sqrt.f64 (/.f64 (cbrt.f64 A) (/.f64 (cbrt.f64 V) (/.f64 1 l)))))
59.0ms	(sqrt.f64 (/.f64 (cbrt.f64 A) (/.f64 (cbrt.f64 V) (/.f64 1 l))))
25.0ms	(/.f64 (cbrt.f64 A) (/.f64 (cbrt.f64 V) (/.f64 1 l)))
1.0ms	(cbrt.f64 A)

Compiler

Compiled 61047 to 24053 computations (60.6% saved)

series1.4s (5.4%)

Error

0.7b

Counts

4 → 33

Calls

4 calls:

607.0ms	(.f64 (.f64 c0 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)))) (sqrt.f64 (/.f64 (cbrt.f64 A) (/.f64 (cbrt.f64 V) (/.f64 1 l)))))
367.0ms	(/.f64 (cbrt.f64 A) (/.f64 (cbrt.f64 V) (/.f64 1 l)))
323.0ms	(sqrt.f64 (/.f64 (cbrt.f64 A) (/.f64 (cbrt.f64 V) (/.f64 1 l))))
74.0ms	(cbrt.f64 A)

Compiler

Compiled 2328 to 1803 computations (22.6% saved)

simplify546.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1700 → 1700

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5120	59054

prune3.1s (11.7%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	1689	11	1700
Fresh	7	11	18
Picked	1	0	1
Done	0	0	0
Total	1697	22	1719

Error

0.0b

Counts

1719 → 22

Compiler

Compiled 55858 to 16653 computations (70.2% saved)

localize35.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (cbrt.f64 A))
0.6b	(cbrt.f64 (cbrt.f64 A))
0.6b	(cbrt.f64 (cbrt.f64 V))
1.4b	(.f64 (.f64 c0 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)))) (.f64 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) (/.f64 (cbrt.f64 (.f64 (cbrt.f64 V) (cbrt.f64 V))) (.f64 (cbrt.f64 (/.f64 1 l)) (cbrt.f64 (/.f64 1 l)))))) (sqrt.f64 (/.f64 (cbrt.f64 (cbrt.f64 A)) (/.f64 (cbrt.f64 (cbrt.f64 V)) (cbrt.f64 (/.f64 1 l)))))))

rewrite330.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

27×	`cbrt-prod_binary64_1132`
16×	`pow1_binary64_1162` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
10×	`add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
8×	`pow-prod-down_binary64_1172` `prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
4×	`add-log-exp_binary64_1140` `sqrt-div_binary64_1118` `associate-*r/_binary64_1043`
3×	`pow1/3_binary64_1183`
1×	`frac-times_binary64_1111` `associate-l/_binary64_1044` `associate-l_binary64_1042` `associate-r_binary64_1041` `-commutative_binary64_1032`

Counts

4 → 67

Calls

4 calls:

173.0ms	(.f64 (.f64 c0 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)))) (.f64 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) (/.f64 (cbrt.f64 (.f64 (cbrt.f64 V) (cbrt.f64 V))) (.f64 (cbrt.f64 (/.f64 1 l)) (cbrt.f64 (/.f64 1 l)))))) (sqrt.f64 (/.f64 (cbrt.f64 (cbrt.f64 A)) (/.f64 (cbrt.f64 (cbrt.f64 V)) (cbrt.f64 (/.f64 1 l)))))))
2.0ms	(cbrt.f64 (cbrt.f64 V))
2.0ms	(cbrt.f64 (cbrt.f64 A))
2.0ms	(cbrt.f64 (cbrt.f64 A))

Compiler

Compiled 4118 to 1608 computations (61% saved)

series991.0ms (3.8%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

660.0ms	(.f64 (.f64 c0 (fabs.f64 (/.f64 (cbrt.f64 A) (cbrt.f64 V)))) (.f64 (sqrt.f64 (/.f64 (.f64 (cbrt.f64 (cbrt.f64 A)) (cbrt.f64 (cbrt.f64 A))) (/.f64 (cbrt.f64 (.f64 (cbrt.f64 V) (cbrt.f64 V))) (.f64 (cbrt.f64 (/.f64 1 l)) (cbrt.f64 (/.f64 1 l)))))) (sqrt.f64 (/.f64 (cbrt.f64 (cbrt.f64 A)) (/.f64 (cbrt.f64 (cbrt.f64 V)) (cbrt.f64 (/.f64 1 l)))))))
103.0ms	(cbrt.f64 (cbrt.f64 A))
100.0ms	(cbrt.f64 (cbrt.f64 V))
98.0ms	(cbrt.f64 (cbrt.f64 A))

Compiler

Compiled 2263 to 1593 computations (29.6% saved)

simplify62.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5120	2727

prune145.0ms (0.6%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	2	19	21
Picked	0	1	1
Done	0	0	0
Total	88	22	110

Error

0.0b

Counts

110 → 22

Compiler

Compiled 4244 to 1710 computations (59.7% saved)

regimes5.0s (19%)

Accuracy

Total 2.4b remaining (98.5%)

Threshold costs 0b (0%)

Compiler

Compiled 69080 to 47605 computations (31.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	79
1	32	79

end0.0ms (0%)

sample7.2s (27.4%)

Algorithm

1×

intervals

Results

285.0ms	8000×	body	128	valid
109.0ms	3015×	body	128	nan
32.0ms	937×	body	128	invalid

Compiler

Compiled 8510 to 5878 computations (30.9% saved)

Details

analyze460.0ms (1.8%)

sample33.0ms (0.1%)

simplify94.0ms (0.4%)

prune2.0ms (0%)

localize7.0ms (0%)

rewrite87.0ms (0.3%)

series324.0ms (1.2%)

simplify77.0ms (0.3%)

prune89.0ms (0.3%)

localize10.0ms (0%)

rewrite601.0ms (2.3%)

series739.0ms (2.8%)

simplify170.0ms (0.7%)

prune435.0ms (1.7%)

localize14.0ms (0.1%)

rewrite4.3s (16.4%)

series1.4s (5.4%)

simplify546.0ms (2.1%)

prune3.1s (11.7%)

localize35.0ms (0.1%)

rewrite330.0ms (1.3%)

series991.0ms (3.8%)

simplify62.0ms (0.2%)

prune145.0ms (0.6%)

regimes5.0s (19%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample7.2s (27.4%)

Profiling