Details

analyze773.0ms (2.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	84
1	60	84
0	4	4
1	4	4

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

Symmetry

(sort V l)

Compiler

Compiled 9 to 9 computations (0% saved)

sample38.0ms (0.1%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
3.0ms	103×	body	128	nan
1.0ms	24×	body	128	invalid

Compiler

Compiled 17 to 21 computations (-23.5% saved)

simplify7.0ms (0%)

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

18.4b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

1.2b	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
4.3b	(/.f64 A (*.f64 V l))
17.0b	(sqrt.f64 (/.f64 A (*.f64 V l)))

rewrite118.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

8.2b

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

Compiler

Compiled 852 to 236 computations (72.3% saved)

series486.0ms (1.6%)

Error

18.4b

Counts

3 → 30

Calls

3 calls:

231.0ms	(.f64 c0 (sqrt.f64 (/.f64 A (.f64 V l))))
156.0ms	(/.f64 A (*.f64 V l))
96.0ms	(sqrt.f64 (/.f64 A (*.f64 V l)))

Compiler

Compiled 798 to 726 computations (9% saved)

simplify77.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4894	1105
1	4894	1105

prune98.0ms (0.3%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	81	15	96
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	16	97

Error

8.2b

Counts

97 → 16

Compiler

Compiled 906 to 349 computations (61.5% saved)

localize8.0ms (0%)

Local error

Found 3 expressions with local error:

1.2b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
3.9b	(*.f64 (/.f64 1 V) (/.f64 A l))
17.0b	(sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))

rewrite182.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

Rules

38×	`add-sqr-sqrt_binary64_1123`
27×	`add-exp-log_binary64_1139`
25×	`times-frac_binary64_1107`
21×	`*-un-lft-identity_binary64_1101`
19×	`add-cube-cbrt_binary64_1136`
17×	`add-cbrt-cube_binary64_1137` `associate-r_binary64_1041`
16×	`associate-l_binary64_1042`
10×	`pow1_binary64_1162`
9×	`prod-exp_binary64_1150`
8×	`div-exp_binary64_1152`
7×	`unswap-sqr_binary64_1069`
6×	`sqrt-div_binary64_1118` `associate-*r/_binary64_1043`
5×	`cbrt-unprod_binary64_1134`
4×	`cbrt-undiv_binary64_1135`
3×	`add-log-exp_binary64_1140` `pow-prod-down_binary64_1172` `frac-times_binary64_1111` `associate-*l/_binary64_1044`
2×	`sqrt-pow1_binary64_1119` `sqrt-prod_binary64_1117` `1-exp_binary64_1145` `rec-exp_binary64_1151` `div-inv_binary64_1098` `*-commutative_binary64_1032`
1×	`pow1/2_binary64_1181`

Counts

3 → 92

Calls

3 calls:

11.0ms	(*.f64 (/.f64 1 V) (/.f64 A l))
9.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
5.0ms	(sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))

Compiler

Compiled 1512 to 806 computations (46.7% saved)

series502.0ms (1.6%)

Error

8.2b

Counts

3 → 30

Calls

3 calls:

237.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 1 V) (/.f64 A l))))
164.0ms	(*.f64 (/.f64 1 V) (/.f64 A l))
97.0ms	(sqrt.f64 (*.f64 (/.f64 1 V) (/.f64 A l)))

Compiler

Compiled 798 to 726 computations (9% saved)

simplify83.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5198	1376

prune136.0ms (0.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	7	7	14
Picked	1	0	1
Done	0	1	1
Total	124	14	138

Error

3.3b

Counts

138 → 14

Compiler

Compiled 1223 to 539 computations (55.9% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 l)
1.2b	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (/.f64 1 V) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 A (cbrt.f64 l)))))
2.4b	(.f64 (/.f64 (/.f64 1 V) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 A (cbrt.f64 l)))
17.0b	(sqrt.f64 (.f64 (/.f64 (/.f64 1 V) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 A (cbrt.f64 l))))

rewrite328.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

2.7b

Rules

79×	`add-exp-log_binary64_1139`
65×	`add-sqr-sqrt_binary64_1123`
63×	`times-frac_binary64_1107`
34×	`add-cbrt-cube_binary64_1137`
33×	`div-exp_binary64_1152`
31×	`*-un-lft-identity_binary64_1101`
28×	`add-cube-cbrt_binary64_1136`
27×	`prod-exp_binary64_1150`
26×	`associate-r_binary64_1041`
20×	`associate-l_binary64_1042`
17×	`cbrt-undiv_binary64_1135`
16×	`cbrt-prod_binary64_1132`
15×	`cbrt-unprod_binary64_1134`
13×	`unswap-sqr_binary64_1069`
11×	`pow1_binary64_1162`
6×	`sqrt-div_binary64_1118` `associate-*r/_binary64_1043`
4×	`add-log-exp_binary64_1140` `1-exp_binary64_1145` `rec-exp_binary64_1151`
3×	`pow-prod-down_binary64_1172` `frac-times_binary64_1111` `associate-*l/_binary64_1044` `div-inv_binary64_1098`
2×	`sqrt-pow1_binary64_1119` `sqrt-prod_binary64_1117` `*-commutative_binary64_1032`
1×	`pow1/2_binary64_1181` `pow1/3_binary64_1183`

Counts

4 → 138

Calls

4 calls:

21.0ms	(.f64 (/.f64 (/.f64 1 V) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 A (cbrt.f64 l)))
18.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (/.f64 1 V) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 A (cbrt.f64 l)))))
11.0ms	(sqrt.f64 (.f64 (/.f64 (/.f64 1 V) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 A (cbrt.f64 l))))
1.0ms	(cbrt.f64 l)

Compiler

Compiled 3551 to 1386 computations (61% saved)

series731.0ms (2.4%)

Error

3.3b

Counts

4 → 33

Calls

4 calls:

259.0ms	(.f64 c0 (sqrt.f64 (.f64 (/.f64 (/.f64 1 V) (*.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 A (cbrt.f64 l)))))
211.0ms	(.f64 (/.f64 (/.f64 1 V) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 A (cbrt.f64 l)))
128.0ms	(cbrt.f64 l)
121.0ms	(sqrt.f64 (.f64 (/.f64 (/.f64 1 V) (.f64 (cbrt.f64 l) (cbrt.f64 l))) (/.f64 A (cbrt.f64 l))))

Compiler

Compiled 1016 to 906 computations (10.8% saved)

simplify111.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4942	2424
1	4942	2424

prune200.0ms (0.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	166	5	171
Fresh	2	10	12
Picked	1	0	1
Done	1	0	1
Total	170	15	185

Error

2.7b

Counts

185 → 15

Compiler

Compiled 2267 to 987 computations (56.5% saved)

localize13.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 l)
1.2b	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 (/.f64 A (cbrt.f64 l)) V)) (fabs.f64 (cbrt.f64 l))))
2.0b	(/.f64 (/.f64 A (cbrt.f64 l)) V)
12.7b	(sqrt.f64 (/.f64 (/.f64 A (cbrt.f64 l)) V))

rewrite1.2s (4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

852×	`times-frac_binary64_1107`
437×	`add-sqr-sqrt_binary64_1123`
406×	`add-cube-cbrt_binary64_1136` `*-un-lft-identity_binary64_1101`
284×	`sqrt-prod_binary64_1117`
223×	`associate-r_binary64_1041`
149×	`cbrt-prod_binary64_1132`
22×	`div-inv_binary64_1098` `associate-/l*_binary64_1046`
14×	`add-exp-log_binary64_1139`
13×	`add-cbrt-cube_binary64_1137`
7×	`pow1_binary64_1162`
6×	`unswap-sqr_binary64_1069`
4×	`add-log-exp_binary64_1140` `rem-sqrt-square_binary64_1114` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
3×	`associate-/r_binary64_1045` `associate-l*_binary64_1042`
2×	`prod-exp_binary64_1150` `cbrt-unprod_binary64_1134`
1×	`pow1/2_binary64_1181` `sqrt-pow1_binary64_1119` `sqrt-div_binary64_1118` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `pow-prod-down_binary64_1172` `associate-r/_binary64_1043` `-commutative_binary64_1032` `pow1/3_binary64_1183`

Counts

4 → 447

Calls

4 calls:

71.0ms	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 (/.f64 A (cbrt.f64 l)) V)) (fabs.f64 (cbrt.f64 l))))
11.0ms	(sqrt.f64 (/.f64 (/.f64 A (cbrt.f64 l)) V))
8.0ms	(/.f64 (/.f64 A (cbrt.f64 l)) V)
1.0ms	(cbrt.f64 l)

Compiler

Compiled 12649 to 2881 computations (77.2% saved)

series1.8s (5.8%)

Error

2.2b

Counts

4 → 33

Calls

4 calls:

778.0ms	(*.f64 c0 (/.f64 (sqrt.f64 (/.f64 (/.f64 A (cbrt.f64 l)) V)) (fabs.f64 (cbrt.f64 l))))
529.0ms	(/.f64 (/.f64 A (cbrt.f64 l)) V)
324.0ms	(sqrt.f64 (/.f64 (/.f64 A (cbrt.f64 l)) V))
126.0ms	(cbrt.f64 l)

Compiler

Compiled 1509 to 1345 computations (10.9% saved)

simplify121.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

480 → 480

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5065	12079

prune808.0ms (2.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	468	12	480
Fresh	9	5	14
Picked	1	0	1
Done	0	0	0
Total	478	17	495

Error

0.0b

Counts

495 → 17

Compiler

Compiled 11332 to 2469 computations (78.2% saved)

regimes21.3s (69.3%)

Accuracy

Total 3.3b remaining (82.2%)

Threshold costs 0b (0%)

Compiler

Compiled 181813 to 128520 computations (29.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	58
1	23	58

end11.0ms (0%)

Compiler: Compiled 102 to 60 computations (41.2% saved)

sample1.5s (5%)

Algorithm

1×

intervals

Results

295.0ms	8000×	body	128	valid
105.0ms	2973×	body	128	nan
38.0ms	865×	body	128	invalid

Compiler

Compiled 452 to 314 computations (30.5% saved)

Details

analyze773.0ms (2.5%)

sample38.0ms (0.1%)

simplify7.0ms (0%)

prune2.0ms (0%)

localize7.0ms (0%)

rewrite118.0ms (0.4%)

series486.0ms (1.6%)

simplify77.0ms (0.3%)

prune98.0ms (0.3%)

localize8.0ms (0%)

rewrite182.0ms (0.6%)

series502.0ms (1.6%)

simplify83.0ms (0.3%)

prune136.0ms (0.4%)

localize13.0ms (0%)

rewrite328.0ms (1.1%)

series731.0ms (2.4%)

simplify111.0ms (0.4%)

prune200.0ms (0.7%)

localize13.0ms (0%)

rewrite1.2s (4%)

series1.8s (5.8%)

simplify121.0ms (0.4%)

prune808.0ms (2.6%)

regimes21.3s (69.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end11.0ms (0%)

sample1.5s (5%)

Profiling