Details

analyze274.0ms (4.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample34.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	245×	body	128	valid
9.0ms	284×	pre	128	true
1.0ms	28×	body	128	nan
1.0ms	11×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify410.0ms (6.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (313.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

27.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
26.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_2146`
14×	`*-un-lft-identity_binary64_2124`
9×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
8×	`add-log-exp_binary64_2163` `add-cube-cbrt_binary64_2159`
6×	`difference-of-squares_binary64_2093` `associate-/l*_binary64_2069` `sqrt-prod_binary64_2140` `times-frac_binary64_2130`
5×	`pow1_binary64_2185`
4×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090`
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 → 74

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series268.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
66.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify89.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune103.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	80	6	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	6	87

Error

0.3b

Counts

87 → 6

Compiler

Compiled 2121 to 1268 computations (40.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite50.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
22×	`times-frac_binary64_2130`
20×	`*-un-lft-identity_binary64_2124`
17×	`cbrt-undiv_binary64_2158` `div-exp_binary64_2175`
13×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
11×	`associate-/l*_binary64_2069`
10×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
8×	`add-log-exp_binary64_2163`
6×	`associate-/r/_binary64_2070`
5×	`distribute-lft-out_binary64_2075` `associate-/r*_binary64_2068`
4×	`pow1_binary64_2185` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121`
2×	`clear-num_binary64_2123` `frac-2neg_binary64_2135`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `sum-log_binary64_2215` `diff-log_binary64_2216` `+-commutative_binary64_2054` `sub-neg_binary64_2117` `associate-/l/_binary64_2071`

Counts

4 → 99

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
11.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series452.0ms (7%)

Counts

4 → 12

Calls

4 calls:

195.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
156.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
67.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune167.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	108	9	117

Error

Counts

117 → 9

Compiler

Compiled 3297 to 2039 computations (38.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.2b	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64_2124`
24×	`times-frac_binary64_2130`
21×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
18×	`associate-r_binary64_2064` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`pow1_binary64_2185`
8×	`distribute-lft-out_binary64_2075` `add-log-exp_binary64_2163`
6×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
4×	`associate-/r/_binary64_2070` `associate-/r*_binary64_2068`
3×	`pow-prod-down_binary64_2195` `cbrt-undiv_binary64_2158` `associate-/l*_binary64_2069` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-exp_binary64_2175`
2×	`div-inv_binary64_2121`
1×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `sum-log_binary64_2215` `-commutative_binary64_2055` `diff-log_binary64_2216` `associate-l_binary64_2065` `+-commutative_binary64_2054` `sub-neg_binary64_2117` `associate-r/_binary64_2066` `frac-2neg_binary64_2135`

Counts

4 → 95

Calls

4 calls:

13.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
8.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series397.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

188.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
112.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
65.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
32.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4961	2612
1	4961	2612

prune146.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	107	9	116

Error

Counts

116 → 9

Compiler

Compiled 3001 to 1918 computations (36.1% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (.f64 a 4))))))) (.f64 a 2))
0.3b	(.f64 c (.f64 (*.f64 a a) 16))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
0.4b	(/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

rewrite80.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
31×	`times-frac_binary64_2130`
27×	`*-un-lft-identity_binary64_2124`
19×	`add-cube-cbrt_binary64_2159` `prod-exp_binary64_2173` `add-sqr-sqrt_binary64_2146` `cbrt-unprod_binary64_2157`
18×	`cbrt-undiv_binary64_2158` `div-exp_binary64_2175`
14×	`associate-/l*_binary64_2069`
13×	`pow1_binary64_2185`
8×	`associate-/r/_binary64_2070` `associate-/r*_binary64_2068`
6×	`pow-prod-down_binary64_2195`
5×	`div-inv_binary64_2121`
4×	`distribute-lft-out_binary64_2075` `add-log-exp_binary64_2163` `flip3-+_binary64_2127` `flip-+_binary64_2098`
3×	`clear-num_binary64_2123` `associate-l_binary64_2065` `associate-/l/_binary64_2071` `frac-2neg_binary64_2135`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `-commutative_binary64_2055` `associate-r*_binary64_2064` `div-sub_binary64_2129`

Counts

4 → 128

Calls

4 calls:

24.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (.f64 a 4))))))) (.f64 a 2))
18.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
10.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
8.0ms	(.f64 c (.f64 (*.f64 a a) 16))

series560.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

255.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
203.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (.f64 a 4))))))) (.f64 a 2))
75.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
27.0ms	(.f64 c (.f64 (*.f64 a a) 16))

simplify124.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4948	6159
1	4948	6159

prune282.0ms (4.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	140	9	149

Error

Counts

149 → 9

Compiler

Compiled 6437 to 3820 computations (40.7% saved)

regimes493.0ms (7.6%)

Accuracy

Total 0.3b remaining (99.9%)

Threshold costs 0.3b (99.9%)

Compiler

Compiled 6996 to 5230 computations (25.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	24
1	60	24

end0.0ms (0%)

sample2.3s (34.8%)

Algorithm

1×

intervals

Results

388.0ms	7673×	body	128	valid
270.0ms	8805×	pre	128	true
43.0ms	805×	body	128	nan
31.0ms	327×	body	256	valid

Compiler

Compiled 1785 to 1336 computations (25.2% saved)

Details

analyze274.0ms (4.2%)

sample34.0ms (0.5%)

simplify410.0ms (6.3%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite36.0ms (0.6%)

series268.0ms (4.2%)

simplify89.0ms (1.4%)

prune103.0ms (1.6%)

localize14.0ms (0.2%)

rewrite50.0ms (0.8%)

series452.0ms (7%)

simplify63.0ms (1%)

prune167.0ms (2.6%)

localize12.0ms (0.2%)

rewrite43.0ms (0.7%)

series397.0ms (6.1%)

simplify82.0ms (1.3%)

prune146.0ms (2.3%)

localize22.0ms (0.3%)

rewrite80.0ms (1.2%)

series560.0ms (8.7%)

simplify124.0ms (1.9%)

prune282.0ms (4.4%)

regimes493.0ms (7.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.3s (34.8%)

Profiling