Details

analyze1.0s (0.2%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample81.0ms (0%)

Algorithm

1×

intervals

Results

23.0ms	39×	body	2048	valid
18.0ms	170×	body	128	valid
10.0ms	25×	body	1024	valid
4.0ms	6×	body	4096	valid
3.0ms	11×	body	512	valid
3.0ms	17×	body	128	invalid
2.0ms	20×	body	128	nan
1.0ms	5×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify745.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (560.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	24

prune10.0ms (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: 33.5b

Counts

2 → 2

Compiler

Compiled 49 to 40 computations (18.4% saved)

localize26.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite61.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_2146`
10×	`pow1_binary64_2185`
9×	`add-exp-log_binary64_2162` `*-un-lft-identity_binary64_2124` `add-cbrt-cube_binary64_2160`
8×	`add-log-exp_binary64_2163`
7×	`add-cube-cbrt_binary64_2159`
4×	`cancel-sign-sub-inv_binary64_2090` `sqrt-prod_binary64_2140`
3×	`flip--_binary64_2099` `pow-prod-down_binary64_2195` `flip3--_binary64_2128` `prod-exp_binary64_2173` `associate-r_binary64_2064` `cbrt-unprod_binary64_2157`
2×	`difference-of-squares_binary64_2093` `sqrt-div_binary64_2141` `diff-log_binary64_2216` `sub-neg_binary64_2117`
1×	`distribute-lft-out--_binary64_2076` `sqrt-pow1_binary64_2142` `-commutative_binary64_2055` `rem-sqrt-square_binary64_2137` `associate-l*_binary64_2065` `pow1/2_binary64_2204`

Counts

4 → 62

Calls

4 calls:

16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
10.0ms	(.f64 (.f64 3 a) c)
10.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series350.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
69.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
29.0ms	(.f64 (.f64 3 a) c)

simplify119.0ms (0%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4872	1226
1	4872	1226

prune871.0ms (0.1%)

Pruning

33 alts after pruning (32 fresh and 1 done)

	Pruned	Kept	Total
New	43	31	74
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	43	33	76

Merged error: 12.5b

Counts

76 → 33

Compiler

Compiled 2382 to 1539 computations (35.4% saved)

localize46.0ms (0%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
22.1b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite195.0ms (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:

71.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
51.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
22.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series1.0s (0.2%)

Counts

4 → 12

Calls

4 calls:

314.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
277.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
254.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
195.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify301.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (200.0ms)

Iter	Nodes	Cost
0	4920	1719
1	4920	1719

prune2.3s (0.4%)

Pruning

52 alts after pruning (50 fresh and 2 done)

	Pruned	Kept	Total
New	66	20	86
Fresh	1	30	31
Picked	0	1	1
Done	0	1	1
Total	67	52	119

Merged error: 12.5b

Counts

119 → 52

Compiler

Compiled 4293 to 2756 computations (35.8% saved)

localize68.0ms (0%)

Local error

Found 4 expressions with local error:

22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
22.1b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))))

rewrite244.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`sqrt-div_binary64_2141`
62×	`sqrt-pow1_binary64_2142`
42×	`pow1_binary64_2185`
30×	`flip--_binary64_2099` `flip3--_binary64_2128`
28×	`frac-times_binary64_2134`
25×	`pow-prod-up_binary64_2194`
24×	`pow1/2_binary64_2204`
14×	`associate-*r/_binary64_2066`
10×	`sqrt-prod_binary64_2140` `add-sqr-sqrt_binary64_2146`
8×	`associate-*l/_binary64_2067`
7×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
5×	`pow-prod-down_binary64_2195` `pow-sqr_binary64_2097`
4×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`rem-sqrt-square_binary64_2137`
1×	`pow-plus_binary64_2187` `pow2_binary64_2205`

Counts

4 → 101

Calls

4 calls:

111.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))))
22.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
21.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
15.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series698.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

253.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))))
161.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
144.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
133.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify270.0ms (0%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (147.0ms)

Iter	Nodes	Cost
0	4891	3844
1	4891	3844

prune3.1s (0.5%)

Pruning

72 alts after pruning (69 fresh and 3 done)

	Pruned	Kept	Total
New	92	21	113
Fresh	1	48	49
Picked	0	1	1
Done	0	2	2
Total	93	72	165

Merged error: 12.5b

Counts

165 → 72

Compiler

Compiled 7902 to 5041 computations (36.2% saved)

localize38.0ms (0%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
22.1b	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite65.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

25.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series419.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

129.0ms	(sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (.f64 1 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
108.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
70.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify226.0ms (0%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (175.0ms)

Iter	Nodes	Cost
0	4903	1708
1	4903	1708

prune1.4s (0.2%)

Pruning

87 alts after pruning (83 fresh and 4 done)

	Pruned	Kept	Total
New	58	16	74
Fresh	1	67	68
Picked	0	1	1
Done	0	3	3
Total	59	87	146

Merged error: 12.5b

Counts

146 → 87

Compiler

Compiled 2633 to 1606 computations (39% saved)

regimes14.3s (2.4%)

Compiler: Compiled 42087 to 30128 computations (28.4% saved)

bsearch8.8min (89.6%)

Steps

Iters	Range	Point
7	1.952482266495952e+148	4.466097784969182e+150	3.771882788472318e+149
8	2.4877006579157012e-281	2.2430424800140092e-278	8.968788607794871e-279
9	-3.586017760766517e+156	-1.690601454612079e+149	-1.3639644452686342e+154

Iters

Range

Point

1.952482266495952e+148

4.466097784969182e+150

3.771882788472318e+149

2.4877006579157012e-281

2.2430424800140092e-278

8.968788607794871e-279

-3.586017760766517e+156

-1.690601454612079e+149

-1.3639644452686342e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify667.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	102	132
1	102	132

end0.0ms (0%)

sample32.5s (5.5%)

Algorithm

1×

intervals

Results

571.0ms	1151×	body	2048	valid
544.0ms	5196×	body	128	valid
291.0ms	717×	body	1024	valid
249.0ms	404×	body	4096	valid
101.0ms	353×	body	512	valid
68.0ms	640×	body	128	nan
42.0ms	418×	body	128	invalid
35.0ms	179×	body	256	valid

Compiler

Compiled 21714 to 14725 computations (32.2% saved)

Pareto

0.12033377012379026

Details

analyze1.0s (0.2%)

sample81.0ms (0%)

simplify745.0ms (0.1%)

prune10.0ms (0%)

localize26.0ms (0%)

rewrite61.0ms (0%)

series350.0ms (0.1%)

simplify119.0ms (0%)

prune871.0ms (0.1%)

localize46.0ms (0%)

rewrite195.0ms (0%)

series1.0s (0.2%)

simplify301.0ms (0.1%)

prune2.3s (0.4%)

localize68.0ms (0%)

rewrite244.0ms (0%)

series698.0ms (0.1%)

simplify270.0ms (0%)

prune3.1s (0.5%)

localize38.0ms (0%)

rewrite65.0ms (0%)

series419.0ms (0.1%)

simplify226.0ms (0%)

prune1.4s (0.2%)

regimes14.3s (2.4%)

bsearch8.8min (89.6%)

simplify667.0ms (0.1%)

end0.0ms (0%)

sample32.5s (5.5%)

Profiling