Details

analyze640.0ms (15.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	154
1	43	154
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%	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 (0.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	15×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	22
1	16	22

prune3.0ms (0.1%)

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

26.4b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.2b	(+.f64 (.f64 a c) (.f64 b d))
25.9b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_4192` `*-un-lft-identity_binary64_4170` `add-cube-cbrt_binary64_4205`
9×	`times-frac_binary64_4176`
7×	`add-log-exp_binary64_4209`
5×	`add-exp-log_binary64_4208` `add-cbrt-cube_binary64_4206`
4×	`flip-+_binary64_4144` `flip3-+_binary64_4173`
3×	`pow1_binary64_4231` `associate-/l_binary64_4115` `associate-/r_binary64_4114`
2×	`associate-/r/_binary64_4116` `+-commutative_binary64_4100` `sum-log_binary64_4261` `associate-/l/_binary64_4117`
1×	`frac-2neg_binary64_4181` `div-inv_binary64_4167` `cbrt-undiv_binary64_4204` `clear-num_binary64_4169` `div-exp_binary64_4221`

Counts

3 → 53

Calls

3 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))

series156.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

91.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
43.0ms	(+.f64 (.f64 a c) (.f64 b d))
22.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify73.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5571	1420

prune78.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	55	7	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	8	63

Error

25.6b

Counts

63 → 8

Compiler

Compiled 1594 to 285 computations (82.1% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (.f64 a c) (.f64 b d))
14.8b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
31.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
31.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_4192`
21×	`*-un-lft-identity_binary64_4170` `add-cube-cbrt_binary64_4205`
18×	`sqrt-prod_binary64_4186` `times-frac_binary64_4176`
6×	`pow1_binary64_4231` `add-exp-log_binary64_4208` `sqrt-div_binary64_4187` `add-cbrt-cube_binary64_4206` `add-log-exp_binary64_4209` `associate-/r*_binary64_4114`
5×	`flip-+_binary64_4144` `flip3-+_binary64_4173`
3×	`associate-/l*_binary64_4115`
2×	`pow1/2_binary64_4250` `associate-/r/_binary64_4116` `sqrt-pow1_binary64_4188` `rem-sqrt-square_binary64_4183` `associate-/l/_binary64_4117`
1×	`frac-2neg_binary64_4181` `div-inv_binary64_4167` `+-commutative_binary64_4100` `cbrt-undiv_binary64_4204` `sum-log_binary64_4261` `clear-num_binary64_4169` `div-exp_binary64_4221`

Counts

4 → 84

Calls

4 calls:

13.0ms	(/.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))

series207.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
38.0ms	(+.f64 (.f64 a c) (.f64 b d))
26.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
24.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify75.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5230	2326

prune97.0ms (2.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	93	11	104

Error

23.9b

Counts

104 → 11

Compiler

Compiled 3371 to 483 computations (85.7% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
14.8b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
31.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
31.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite68.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64_4192`
76×	`times-frac_binary64_4176`
53×	`*-un-lft-identity_binary64_4170`
47×	`sqrt-prod_binary64_4186` `add-cube-cbrt_binary64_4205`
28×	`add-exp-log_binary64_4208`
24×	`associate-l_binary64_4111` `associate-r_binary64_4110`
18×	`add-cbrt-cube_binary64_4206`
15×	`unswap-sqr_binary64_4138`
10×	`sqrt-div_binary64_4187`
9×	`div-exp_binary64_4221`
8×	`pow1_binary64_4231` `prod-exp_binary64_4219`
6×	`flip-+_binary64_4144` `associate-/r/_binary64_4116` `flip3-+_binary64_4173` `associate-/r*_binary64_4114`
5×	`cbrt-undiv_binary64_4204`
4×	`cbrt-unprod_binary64_4203` `add-log-exp_binary64_4209`
3×	`associate-/l*_binary64_4115` `div-inv_binary64_4167`
2×	`1-exp_binary64_4214` `rec-exp_binary64_4220` `pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `rem-sqrt-square_binary64_4183` `associate-/l/_binary64_4117`
1×	`frac-times_binary64_4180` `associate-r/_binary64_4112` `associate-l/_binary64_4113` `frac-2neg_binary64_4181` `*-commutative_binary64_4101` `pow-prod-down_binary64_4241` `clear-num_binary64_4169`

Counts

4 → 160

Calls

4 calls:

29.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
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)))

series321.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
129.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
28.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
25.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify121.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4969	5537
1	4969	5537

prune167.0ms (4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	172	11	183

Error

23.9b

Counts

183 → 11

Compiler

Compiled 6214 to 913 computations (85.3% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.2b	(+.f64 (.f64 a c) (.f64 b d))
0.5b	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d))))
25.5b	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d)))

rewrite42.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64_4176`
56×	`add-sqr-sqrt_binary64_4192` `*-un-lft-identity_binary64_4170` `add-cube-cbrt_binary64_4205`
18×	`associate-/r*_binary64_4114`
17×	`add-exp-log_binary64_4208`
11×	`add-cbrt-cube_binary64_4206` `associate-/r/_binary64_4116`
8×	`flip-+_binary64_4144` `flip3-+_binary64_4173` `add-log-exp_binary64_4209` `div-exp_binary64_4221`
6×	`associate-/l*_binary64_4115` `div-inv_binary64_4167`
5×	`pow1_binary64_4231`
4×	`cbrt-undiv_binary64_4204`
2×	`1-exp_binary64_4214` `frac-2neg_binary64_4181` `rec-exp_binary64_4220` `+-commutative_binary64_4100` `sum-log_binary64_4261` `associate-/l/_binary64_4117` `clear-num_binary64_4169`
1×	`pow-flip_binary64_4244` `inv-pow_binary64_4255`

Counts

4 → 137

Calls

4 calls:

11.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d))))
9.0ms	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d)))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

series259.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

136.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d))))
64.0ms	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (+.f64 (.f64 a c) (.f64 b d)))
36.0ms	(+.f64 (.f64 a c) (.f64 b d))
22.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify112.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5008	4822

prune121.0ms (2.9%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	3	5	8
Picked	0	1	1
Done	0	2	2
Total	150	10	160

Error

23.9b

Counts

160 → 10

Compiler

Compiled 4192 to 674 computations (83.9% saved)

regimes333.0ms (7.9%)

Accuracy

Total 2.2b remaining (8.9%)

Threshold costs 0b (0%)

Compiler

Compiled 4325 to 2343 computations (45.8% saved)

bsearch2.0ms (0.1%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	82
1	39	82

end0.0ms (0%)

sample1.2s (28%)

Algorithm

1×

intervals

Results

354.0ms	8000×	body	128	valid
25.0ms	519×	body	128	invalid

Compiler

Compiled 934 to 497 computations (46.8% saved)

Details

analyze640.0ms (15.3%)

sample22.0ms (0.5%)

simplify11.0ms (0.3%)

prune3.0ms (0.1%)

localize11.0ms (0.3%)

rewrite22.0ms (0.5%)

series156.0ms (3.7%)

simplify73.0ms (1.7%)

prune78.0ms (1.9%)

localize13.0ms (0.3%)

rewrite33.0ms (0.8%)

series207.0ms (4.9%)

simplify75.0ms (1.8%)

prune97.0ms (2.3%)

localize18.0ms (0.4%)

rewrite68.0ms (1.6%)

series321.0ms (7.7%)

simplify121.0ms (2.9%)

prune167.0ms (4%)

localize12.0ms (0.3%)

rewrite42.0ms (1%)

series259.0ms (6.2%)

simplify112.0ms (2.7%)

prune121.0ms (2.9%)

regimes333.0ms (7.9%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (28%)

Profiling