Details

analyze787.0ms (14.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample38.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	185×	body	128	valid
8.0ms	32×	body	2048	valid
5.0ms	256×	pre	128	true
3.0ms	17×	body	1024	valid
3.0ms	9×	body	4096	valid
1.0ms	6×	body	512	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify95.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 15.4b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
1.3b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
14.8b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite45.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`pow1_binary64_2185` `add-log-exp_binary64_2163`
7×	`*-un-lft-identity_binary64_2124`
6×	`add-sqr-sqrt_binary64_2146`
5×	`add-cube-cbrt_binary64_2159`
4×	`sqrt-prod_binary64_2140` `sqrt-div_binary64_2141` `flip3-+_binary64_2127` `flip-+_binary64_2098` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`sqrt-pow1_binary64_2142`
2×	`sum-log_binary64_2215` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `associate-*r/_binary64_2066`
1×	`pow-prod-down_binary64_2195` `distribute-lft-out_binary64_2075` `rem-sqrt-square_binary64_2137`

Counts

4 → 51

Calls

4 calls:

14.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
13.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
6.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))

series191.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
41.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
28.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
27.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4937	1285
1	4937	1285

prune105.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	52	11	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	11	64

Merged error: 15.1b

Counts

64 → 11

Compiler

Compiled 1701 to 1164 computations (31.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(exp.f64 (log.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
1.3b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
2.4b	(log.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))
14.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite54.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_2124`
9×	`add-sqr-sqrt_binary64_2146`
8×	`log-prod_binary64_2210` `add-cube-cbrt_binary64_2159`
7×	`pow1_binary64_2185`
6×	`add-log-exp_binary64_2163`
5×	`add-exp-log_binary64_2162`
4×	`exp-prod_binary64_2176` `flip3-+_binary64_2127` `log-div_binary64_2211` `flip-+_binary64_2098` `add-cbrt-cube_binary64_2160` `exp-sum_binary64_2170`
3×	`sqrt-prod_binary64_2140` `distribute-lft-out_binary64_2075`
2×	`log-pow_binary64_2213` `exp-diff_binary64_2172` `sqrt-div_binary64_2141`
1×	`rem-log-exp_binary64_2165` `sum-log_binary64_2215` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `rem-exp-log_binary64_2164` `+-commutative_binary64_2054` `pow1/2_binary64_2204`

Counts

4 → 60

Calls

4 calls:

17.0ms	(exp.f64 (log.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
13.0ms	(log.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))
13.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series249.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(exp.f64 (log.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
72.0ms	(log.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))
40.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
28.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify107.0ms (2%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4864	1666
1	4864	1666

prune112.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 7.4b

Counts

83 → 5

Compiler

Compiled 1926 to 1340 computations (30.4% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.3b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
14.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
14.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
14.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2146`
9×	`sqrt-prod_binary64_2140` `*-un-lft-identity_binary64_2124`
7×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159`
6×	`sqrt-div_binary64_2141` `add-log-exp_binary64_2163`
4×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204`
1×	`sum-log_binary64_2215` `distribute-lft-out_binary64_2075` `+-commutative_binary64_2054`

Counts

4 → 57

Calls

4 calls:

13.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series114.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
25.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
24.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
24.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify114.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4841	1276
1	4841	1276

prune200.0ms (3.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	69	5	74

Merged error: 7.4b

Counts

74 → 5

Compiler

Compiled 4305 to 2960 computations (31.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
10.5b	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
14.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
14.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite61.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`sqrt-prod_binary64_2140`
58×	`add-sqr-sqrt_binary64_2146`
34×	`sqrt-pow1_binary64_2142`
29×	`pow1_binary64_2185`
28×	`sqrt-div_binary64_2141`
20×	`*-un-lft-identity_binary64_2124`
18×	`add-cube-cbrt_binary64_2159` `pow1/2_binary64_2204`
15×	`swap-sqr_binary64_2091`
10×	`rem-sqrt-square_binary64_2137`
9×	`unswap-sqr_binary64_2092` `pow-prod-up_binary64_2194` `associate-l_binary64_2065` `flip3-+_binary64_2127` `associate-r_binary64_2064` `flip-+_binary64_2098`
6×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`pow-prod-down_binary64_2195` `pow-sqr_binary64_2097`
4×	`sqr-abs_binary64_2139` `frac-times_binary64_2134`
2×	`associate-l/_binary64_2067` `associate-r/_binary64_2066`
1×	`sqrt-unprod_binary64_2144` `sum-log_binary64_2215` `*-commutative_binary64_2055` `distribute-lft-out_binary64_2075` `prod-exp_binary64_2173` `pow-plus_binary64_2187` `+-commutative_binary64_2054` `rem-square-sqrt_binary64_2136` `pow2_binary64_2205` `cbrt-unprod_binary64_2157`

Counts

4 → 129

Calls

4 calls:

20.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
10.0ms	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series120.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

45.0ms	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
27.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
24.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
24.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify107.0ms (2%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4925	2792
1	4925	2792

prune200.0ms (3.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	141	5	146

Merged error: 7.4b

Counts

146 → 5

Compiler

Compiled 4182 to 2723 computations (34.9% saved)

regimes508.0ms (9.6%)

Compiler: Compiled 6224 to 4990 computations (19.8% saved)

bsearch2.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	66	73
1	66	73

end0.0ms (0%)

sample1.9s (36.2%)

Algorithm

1×

intervals

Results

308.0ms	6062×	body	128	valid
198.0ms	774×	body	2048	valid
160.0ms	8000×	pre	128	true
106.0ms	527×	body	1024	valid
81.0ms	260×	body	4096	valid
39.0ms	247×	body	512	valid
13.0ms	130×	body	256	valid

Compiler

Compiled 911 to 722 computations (20.7% saved)

Details

analyze787.0ms (14.8%)

sample38.0ms (0.7%)

simplify95.0ms (1.8%)

prune3.0ms (0%)

localize11.0ms (0.2%)

rewrite45.0ms (0.8%)

series191.0ms (3.6%)

simplify69.0ms (1.3%)

prune105.0ms (2%)

localize13.0ms (0.3%)

rewrite54.0ms (1%)

series249.0ms (4.7%)

simplify107.0ms (2%)

prune112.0ms (2.1%)

localize19.0ms (0.4%)

rewrite39.0ms (0.7%)

series114.0ms (2.1%)

simplify114.0ms (2.2%)

prune200.0ms (3.8%)

localize14.0ms (0.3%)

rewrite61.0ms (1.1%)

series120.0ms (2.3%)

simplify107.0ms (2%)

prune200.0ms (3.8%)

regimes508.0ms (9.6%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.9s (36.2%)

Profiling