Details

analyze520.0ms (5.6%)

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%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample22.0ms (0.2%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	12×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify99.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	22
1	16	22

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

28.9b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 6 expressions with local error:

28.4b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
0.9b	(+.f64 (.f64 a c) (.f64 b d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.9b	(+.f64 (.f64 a c) (.f64 b d))
28.4b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1758` `add-cube-cbrt_binary64_1771` `*-un-lft-identity_binary64_1736`
9×	`times-frac_binary64_1742`
7×	`add-log-exp_binary64_1775`
5×	`add-cbrt-cube_binary64_1772` `add-exp-log_binary64_1774`
4×	`flip-+_binary64_1710` `flip3-+_binary64_1739`
3×	`pow1_binary64_1797` `associate-/l_binary64_1681` `associate-/r_binary64_1680`
2×	`associate-/l/_binary64_1683` `sum-log_binary64_1827` `associate-/r/_binary64_1682` `+-commutative_binary64_1666`
1×	`cbrt-undiv_binary64_1770` `frac-2neg_binary64_1747` `div-exp_binary64_1787` `clear-num_binary64_1735` `div-inv_binary64_1733`

Counts

3 → 53

Calls

6 calls:

9.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))
0.0ms	(+.f64 (.f64 c c) (.f64 d d))
0.0ms	(+.f64 (.f64 a c) (.f64 b d))

series546.0ms (5.8%)

Counts

3 → 63

Calls

3 calls:

321.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
138.0ms	(+.f64 (.f64 a c) (.f64 b d))
86.0ms	(+.f64 (.f64 c c) (.f64 d d))

Compiler

Compiled 1383 to 1146 computations (17.1% saved)

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4952	2131
1	4952	2131

prune172.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	107	9	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	9	117

Error

6.1b

Counts

117 → 9

Compiler

Compiled 2310 to 308 computations (86.7% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.9b	(+.f64 (.f64 a c) (.f64 b d))
0.1b	(/.f64 (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.9b	(+.f64 (.f64 a c) (.f64 b d))
18.3b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
33.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
33.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_1758`
21×	`add-cube-cbrt_binary64_1771` `*-un-lft-identity_binary64_1736`
18×	`times-frac_binary64_1742` `sqrt-prod_binary64_1752`
6×	`pow1_binary64_1797` `add-cbrt-cube_binary64_1772` `add-exp-log_binary64_1774` `add-log-exp_binary64_1775` `sqrt-div_binary64_1753` `associate-/r*_binary64_1680`
5×	`flip-+_binary64_1710` `flip3-+_binary64_1739`
3×	`associate-/l*_binary64_1681`
2×	`associate-/l/_binary64_1683` `rem-sqrt-square_binary64_1749` `associate-/r/_binary64_1682` `sqrt-pow1_binary64_1754` `pow1/2_binary64_1816`
1×	`sum-log_binary64_1827` `cbrt-undiv_binary64_1770` `frac-2neg_binary64_1747` `div-exp_binary64_1787` `clear-num_binary64_1735` `div-inv_binary64_1733` `+-commutative_binary64_1666`

Counts

4 → 84

Calls

8 calls:

10.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))
0.0ms	(+.f64 (.f64 c c) (.f64 d d))

series826.0ms (8.9%)

Counts

4 → 94

Calls

4 calls:

421.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
144.0ms	(+.f64 (.f64 a c) (.f64 b d))
131.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
130.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 3540 to 2496 computations (29.5% saved)

simplify74.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4973	3666
1	4973	3666

prune147.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	178	9	187

Error

6.1b

Counts

187 → 9

Compiler

Compiled 5402 to 787 computations (85.4% saved)

localize20.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(/.f64 (cbrt.f64 (+.f64 (.f64 a c) (.f64 b d))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
0.3b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 (.f64 a c) (.f64 b d))) (cbrt.f64 (+.f64 (.f64 a c) (.f64 b d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (cbrt.f64 (+.f64 (.f64 a c) (.f64 b d))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
18.9b	(cbrt.f64 (+.f64 (.f64 a c) (.f64 b d)))
18.9b	(cbrt.f64 (+.f64 (.f64 a c) (.f64 b d)))
33.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
33.6b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite24.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_1758`
8×	`add-cube-cbrt_binary64_1771` `*-un-lft-identity_binary64_1736`
6×	`sqrt-prod_binary64_1752` `pow1_binary64_1797` `cbrt-prod_binary64_1767`
4×	`add-cbrt-cube_binary64_1772` `add-exp-log_binary64_1774` `add-log-exp_binary64_1775` `flip-+_binary64_1710` `cbrt-div_binary64_1768` `flip3-+_binary64_1739` `sqrt-div_binary64_1753`
2×	`pow1/3_binary64_1818` `rem-sqrt-square_binary64_1749` `sqrt-pow1_binary64_1754` `pow1/2_binary64_1816`

Counts

4 → 56

Calls

8 calls:

4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(cbrt.f64 (+.f64 (.f64 a c) (.f64 b d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(cbrt.f64 (+.f64 (.f64 a c) (.f64 b d)))
0.0ms	(+.f64 (.f64 c c) (.f64 d d))

series1.1s (11.9%)

Counts

4 → 94

Calls

4 calls:

420.0ms	(cbrt.f64 (+.f64 (.f64 a c) (.f64 b d)))
413.0ms	(cbrt.f64 (+.f64 (.f64 a c) (.f64 b d)))
139.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
138.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 8188 to 4644 computations (43.3% saved)

simplify57.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4995	3502
1	4995	3502

prune192.0ms (2.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	150	9	159

Error

6.1b

Counts

159 → 9

Compiler

Compiled 7931 to 1134 computations (85.7% saved)

localize16.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.4b	(.f64 (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (cbrt.f64 (+.f64 (.f64 c c) (*.f64 d d))))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
14.6b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
34.7b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
34.7b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
34.7b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite66.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-exp-log_binary64_1774`
43×	`add-sqr-sqrt_binary64_1758`
33×	`times-frac_binary64_1742`
25×	`*-un-lft-identity_binary64_1736`
24×	`associate-r_binary64_1676`
22×	`add-cube-cbrt_binary64_1771`
21×	`cbrt-prod_binary64_1767`
20×	`cbrt-div_binary64_1768` `prod-exp_binary64_1785`
18×	`add-cbrt-cube_binary64_1772`
15×	`associate-l_binary64_1677` `div-exp_binary64_1787`
10×	`flip-+_binary64_1710` `associate-/r/_binary64_1682` `flip3-+_binary64_1739`
9×	`unswap-sqr_binary64_1704`
8×	`cbrt-unprod_binary64_1769`
7×	`cbrt-undiv_binary64_1770`
6×	`pow1_binary64_1797`
5×	`frac-times_binary64_1746`
4×	`1-exp_binary64_1780` `add-log-exp_binary64_1775` `rec-exp_binary64_1786`
3×	`pow1/3_binary64_1818` `associate-l/_binary64_1679` `associate-r/_binary64_1678`
2×	`div-inv_binary64_1733`
1×	`*-commutative_binary64_1667` `pow-prod-down_binary64_1807`

Counts

4 → 119

Calls

8 calls:

34.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
6.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
0.0ms	(+.f64 (.f64 c c) (.f64 d d))

series1.1s (11.7%)

Counts

4 → 81

Calls

4 calls:

348.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
254.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
245.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
240.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 3858 to 2790 computations (27.7% saved)

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4953	6484
1	4953	6484

prune215.0ms (2.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	200	9	209

Error

6.1b

Counts

209 → 9

Compiler

Compiled 7908 to 1485 computations (81.2% saved)

simplify20.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	246	1298
1	246	1298

regimes668.0ms (7.2%)

Accuracy

Total 10.4b remaining (68%)

Threshold costs 0b (0%)

Compiler

Compiled 3460 to 1952 computations (43.6% saved)

bsearch128.0ms (1.4%)

Steps

Iters	Range		Point
6	3.0079263460503392e+141	2.9088058847187696e+142	1.4163550870851477e+142
8	3.351979612061897e-129	7.771908528663381e-126	1.9690354844540234e-126
7	-5.032597015020011e-90	-1.1218585152763866e-91	-9.83945259871375e-91
2	-3276.227314365947	-2968.9548182272824	-3084.182004279282
9	-1.4378203688264434e+28	-2.179227465769176e+22	-2.2148262768226444e+22
7	-4.794225511072451e+135	-5.807041215597531e+133	-4.7218745403061054e+135
9	-6.0645011590064754e+150	-1.2420786890435458e+143	-1.266447775026859e+143

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	215
1	50	215

end0.0ms (0%)

sample3.1s (32.9%)

Algorithm

1×

intervals

Results

333.0ms	8000×	body	128	valid
18.0ms	456×	body	128	invalid

Compiler

Compiled 2929 to 1558 computations (46.8% saved)

Pareto

0.1313405833802934

Details

analyze520.0ms (5.6%)

sample22.0ms (0.2%)

simplify99.0ms (1.1%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite22.0ms (0.2%)

series546.0ms (5.8%)

simplify71.0ms (0.8%)

prune172.0ms (1.8%)

localize13.0ms (0.1%)

rewrite31.0ms (0.3%)

series826.0ms (8.9%)

simplify74.0ms (0.8%)

prune147.0ms (1.6%)

localize20.0ms (0.2%)

rewrite24.0ms (0.3%)

series1.1s (11.9%)

simplify57.0ms (0.6%)

prune192.0ms (2.1%)

localize16.0ms (0.2%)

rewrite66.0ms (0.7%)

series1.1s (11.7%)

simplify103.0ms (1.1%)

prune215.0ms (2.3%)

simplify20.0ms (0.2%)

regimes668.0ms (7.2%)

bsearch128.0ms (1.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.1s (32.9%)

Profiling