Details

analyze2.3s (0.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample149.0ms (0%)

Algorithm

1×

intervals

Results

53.0ms	185×	body	128	valid
38.0ms	34×	body	2048	valid
10.0ms	16×	body	1024	valid
4.0ms	6×	body	4096	valid
2.0ms	7×	body	512	valid
2.0ms	20×	body	128	nan
2.0ms	17×	body	128	invalid
2.0ms	8×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify1.6s (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.2s)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune19.0ms (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

Merged error: 30.0b

Counts

2 → 2

Compiler

Compiled 49 to 40 computations (18.4% saved)

localize55.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
0.8b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite159.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_2124`
10×	`add-log-exp_binary64_2163`
9×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
8×	`add-sqr-sqrt_binary64_2146`
7×	`add-cube-cbrt_binary64_2159`
6×	`distribute-lft-out_binary64_2075`
5×	`associate-/l*_binary64_2069` `pow1_binary64_2185` `times-frac_binary64_2130`
3×	`sqrt-prod_binary64_2140` `distribute-rgt-neg-in_binary64_2082`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `cbrt-undiv_binary64_2158` `associate-+l-_binary64_2059` `sum-log_binary64_2215` `sqrt-div_binary64_2141` `flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/l/_binary64_2071` `div-exp_binary64_2175` `neg-sub0_binary64_2119`
1×	`clear-num_binary64_2123` `cancel-sign-sub-inv_binary64_2090` `neg-log_binary64_2217` `sqrt-pow1_binary64_2142` `associate-/r*_binary64_2068` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `prod-exp_binary64_2173` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `div-sub_binary64_2129` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`

Counts

4 → 70

Calls

4 calls:

56.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
37.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series1.1s (0.2%)

Counts

4 → 12

Calls

4 calls:

451.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
277.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
235.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
127.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify237.0ms (0%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (162.0ms)

Iter	Nodes	Cost
0	5581	1826

prune1.5s (0.3%)

Pruning

43 alts after pruning (42 fresh and 1 done)

	Pruned	Kept	Total
New	41	41	82
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	41	43	84

Merged error: 5.1b

Counts

84 → 43

Compiler

Compiled 2991 to 1785 computations (40.3% saved)

localize65.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a 2))
0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite129.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_2146`
15×	`*-un-lft-identity_binary64_2124`
9×	`sqrt-prod_binary64_2140` `add-cube-cbrt_binary64_2159` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
8×	`add-log-exp_binary64_2163`
7×	`cancel-sign-sub-inv_binary64_2090`
6×	`difference-of-squares_binary64_2093` `associate-/l*_binary64_2069` `times-frac_binary64_2130`
5×	`pow1_binary64_2185`
4×	`flip--_binary64_2099` `flip3--_binary64_2128`
3×	`distribute-lft-out--_binary64_2076`
2×	`cbrt-undiv_binary64_2158` `sqrt-div_binary64_2141` `diff-log_binary64_2216` `sub-neg_binary64_2117` `associate-/l/_binary64_2071` `div-exp_binary64_2175`
1×	`clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `associate-/r*_binary64_2068` `rem-sqrt-square_binary64_2137` `prod-exp_binary64_2173` `pow1/2_binary64_2204` `div-sub_binary64_2129` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`

Counts

4 → 77

Calls

4 calls:

36.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
33.0ms	(/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a 2))
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series883.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

424.0ms	(/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 a 2))
262.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
139.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
57.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify157.0ms (0%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4926	2111
1	4926	2111

prune3.0s (0.5%)

Pruning

81 alts after pruning (79 fresh and 2 done)

	Pruned	Kept	Total
New	47	42	89
Fresh	4	37	41
Picked	0	1	1
Done	0	1	1
Total	51	81	132

Merged error: 5.1b

Counts

132 → 81

Compiler

Compiled 4458 to 2875 computations (35.5% saved)

localize60.0ms (0%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.4b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))

rewrite133.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`sqrt-pow1_binary64_2142` `sqrt-div_binary64_2141`
22×	`pow1_binary64_2185`
11×	`pow1/2_binary64_2204`
9×	`flip--_binary64_2099` `flip3--_binary64_2128`
8×	`add-sqr-sqrt_binary64_2146`
7×	`sqrt-prod_binary64_2140`
6×	`add-log-exp_binary64_2163` `add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
5×	`pow-prod-up_binary64_2194`
4×	`frac-times_binary64_2134` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`pow-prod-down_binary64_2195` `rem-sqrt-square_binary64_2137` `pow-sqr_binary64_2097`
2×	`associate-l/_binary64_2067` `associate-r/_binary64_2066`
1×	`cancel-sign-sub-inv_binary64_2090` `diff-log_binary64_2216` `pow-plus_binary64_2187` `sub-neg_binary64_2117` `pow2_binary64_2205`

Counts

4 → 74

Calls

4 calls:

46.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
23.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series892.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

272.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
249.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
238.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
133.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify243.0ms (0%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (164.0ms)

Iter	Nodes	Cost
0	5016	1719

prune4.5s (0.8%)

Pruning

98 alts after pruning (95 fresh and 3 done)

	Pruned	Kept	Total
New	67	19	86
Fresh	2	76	78
Picked	0	1	1
Done	0	2	2
Total	69	98	167

Merged error: 5.1b

Counts

167 → 98

Compiler

Compiled 5873 to 3726 computations (36.6% saved)

localize72.0ms (0%)

Local error

Found 4 expressions with local error:

20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
20.4b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
20.4b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))

rewrite268.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

128×	`sqrt-div_binary64_2141`
83×	`sqrt-pow1_binary64_2142`
57×	`pow1_binary64_2185`
35×	`flip--_binary64_2099` `flip3--_binary64_2128`
32×	`pow1/2_binary64_2204` `frac-times_binary64_2134`
30×	`pow-prod-up_binary64_2194`
16×	`associate-*r/_binary64_2066`
10×	`associate-*l/_binary64_2067`
8×	`pow-prod-down_binary64_2195` `sqrt-prod_binary64_2140` `add-sqr-sqrt_binary64_2146` `pow-sqr_binary64_2097`
6×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
4×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`rem-sqrt-square_binary64_2137`
2×	`pow-plus_binary64_2187` `pow2_binary64_2205`

Counts

4 → 118

Calls

4 calls:

93.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
47.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
27.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series901.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

240.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
237.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
221.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
203.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify368.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (199.0ms)

Iter	Nodes	Cost
0	4999	4243
1	4999	4243

prune5.8s (1%)

Pruning

122 alts after pruning (118 fresh and 4 done)

	Pruned	Kept	Total
New	101	29	130
Fresh	5	89	94
Picked	0	1	1
Done	0	3	3
Total	106	122	228

Merged error: 5.1b

Counts

228 → 122

Compiler

Compiled 5980 to 3347 computations (44% saved)

regimes22.6s (3.8%)

Compiler: Compiled 31029 to 21712 computations (30% saved)

bsearch9.2min (92.1%)

Steps

Iters	Range		Point
7	5.077603163681316e+86	3.0675607530650454e+88	1.0076800180697053e+87
8	1.1967310277021378e-191	8.34259427963184e-189	2.43077786380867e-190
6	-5.59945793777678e+90	-4.402997549349525e+89	-4.787296627726359e+90

Compiler

Compiled 1 to 3 computations (-200% saved)

Details

analyze2.3s (0.4%)

sample149.0ms (0%)

simplify1.6s (0.3%)

prune19.0ms (0%)

localize55.0ms (0%)

rewrite159.0ms (0%)

series1.1s (0.2%)

simplify237.0ms (0%)

prune1.5s (0.3%)

localize65.0ms (0%)

rewrite129.0ms (0%)

series883.0ms (0.1%)

simplify157.0ms (0%)

prune3.0s (0.5%)

localize60.0ms (0%)

rewrite133.0ms (0%)

series892.0ms (0.1%)

simplify243.0ms (0%)

prune4.5s (0.8%)

localize72.0ms (0%)

rewrite268.0ms (0%)

series901.0ms (0.2%)

simplify368.0ms (0.1%)

prune5.8s (1%)

regimes22.6s (3.8%)

bsearch9.2min (92.1%)

Profiling