Details

analyze475.0ms (7.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5132	96
0	3	3
1	3	3

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)

sample35.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	247×	body	128	valid
8.0ms	275×	pre	128	true
1.0ms	19×	body	128	nan
1.0ms	9×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify317.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (312.0ms)

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

29.0b

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))
29.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite34.0ms (0.5%)

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))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series266.0ms (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))
67.0ms	(-.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)))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify91.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune104.0ms (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

0.4b

Counts

87 → 6

Compiler

Compiled 2135 to 1276 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)))))

rewrite53.0ms (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))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
11.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series448.0ms (7%)

Counts

4 → 12

Calls

4 calls:

197.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
155.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
61.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune164.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	8	111
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Error

0.0b

Counts

117 → 8

Compiler

Compiled 3301 to 2036 computations (38.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite48.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
21×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
9×	`cbrt-undiv_binary64_2158` `pow1_binary64_2185` `*-un-lft-identity_binary64_2124` `div-exp_binary64_2175`
8×	`add-log-exp_binary64_2163`
5×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
4×	`associate-l_binary64_2065` `associate-*l/_binary64_2067`
3×	`pow-prod-down_binary64_2195` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`associate-/r/_binary64_2070` `distribute-lft-out_binary64_2075`
1×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `sum-log_binary64_2215` `associate-/l_binary64_2069` `-commutative_binary64_2055` `associate-/r_binary64_2068` `diff-log_binary64_2216` `+-commutative_binary64_2054` `sub-neg_binary64_2117` `associate-r*_binary64_2064` `div-inv_binary64_2121` `times-frac_binary64_2130` `frac-2neg_binary64_2135`

Counts

4 → 78

Calls

4 calls:

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

series358.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

156.0ms	(/.f64 (.f64 a (.f64 c -4)) (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (*.f64 a 2)))
108.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (*.f64 a 2))
57.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
37.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify95.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4939	2276
1	4939	2276

prune117.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	91	7	98

Error

Counts

98 → 7

Compiler

Compiled 2654 to 1600 computations (39.7% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (.f64 (+.f64 b (sqrt.f64 (/.f64 (+.f64 (.f64 -64 (pow.f64 (.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))) (.f64 a 2)))
0.4b	(/.f64 (+.f64 (.f64 -64 (pow.f64 (.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
0.7b	(pow.f64 (*.f64 a c) 3)

rewrite72.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
25×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
16×	`pow1_binary64_2185`
14×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
10×	`cbrt-undiv_binary64_2158` `times-frac_binary64_2130` `div-exp_binary64_2175`
7×	`pow-prod-down_binary64_2195`
4×	`associate-/r/_binary64_2070` `associate-/l_binary64_2069` `associate-/r_binary64_2068` `add-log-exp_binary64_2163` `distribute-rgt-in_binary64_2074` `associate-*r/_binary64_2066` `flip3-+_binary64_2127` `flip-+_binary64_2098` `distribute-lft-in_binary64_2073`
3×	`pow-unpow_binary64_2201` `associate-l_binary64_2065`
2×	`clear-num_binary64_2123` `pow-pow_binary64_2196` `pow-exp_binary64_2192` `associate-*l/_binary64_2067` `div-inv_binary64_2121` `associate-/l/_binary64_2071` `frac-2neg_binary64_2135` `rem-cube-cbrt_binary64_2147`
1×	`unpow3_binary64_2190` `unpow-prod-down_binary64_2203` `cube-mult_binary64_2154` `-commutative_binary64_2055` `sqr-pow_binary64_2096` `cube-prod_binary64_2152` `pow-to-exp_binary64_2193` `associate-r*_binary64_2064`

Counts

4 → 113

Calls

4 calls:

25.0ms	(/.f64 (.f64 a (.f64 c -4)) (.f64 (+.f64 b (sqrt.f64 (/.f64 (+.f64 (.f64 -64 (pow.f64 (.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))) (.f64 a 2)))
13.0ms	(/.f64 (+.f64 (.f64 -64 (pow.f64 (.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
11.0ms	(.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))
4.0ms	(pow.f64 (*.f64 a c) 3)

series505.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

239.0ms	(/.f64 (.f64 a (.f64 c -4)) (.f64 (+.f64 b (sqrt.f64 (/.f64 (+.f64 (.f64 -64 (pow.f64 (.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))) (.f64 a 2)))
160.0ms	(/.f64 (+.f64 (.f64 -64 (pow.f64 (.f64 a c) 3)) (pow.f64 b 6)) (+.f64 (pow.f64 b 4) (.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
68.0ms	(.f64 c (.f64 (.f64 a 4) (+.f64 (.f64 b b) (.f64 c (.f64 a 4)))))
37.0ms	(pow.f64 (*.f64 a c) 3)

simplify95.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4987	5188
1	4987	5188

prune315.0ms (4.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	125	7	132

Error

Counts

132 → 7

Compiler

Compiled 6546 to 4179 computations (36.2% saved)

regimes469.0ms (7.4%)

Accuracy

Total 0.3b remaining (99.5%)

Threshold costs 0.3b (99.5%)

Compiler

Compiled 6560 to 4894 computations (25.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample2.2s (34%)

Algorithm

1×

intervals

Results

380.0ms	7709×	body	128	valid
269.0ms	8823×	pre	128	true
37.0ms	823×	body	128	nan
27.0ms	291×	body	256	valid

Compiler

Compiled 1676 to 1252 computations (25.3% saved)

Details

analyze475.0ms (7.5%)

sample35.0ms (0.5%)

simplify317.0ms (5%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite34.0ms (0.5%)

series266.0ms (4.2%)

simplify91.0ms (1.4%)

prune104.0ms (1.6%)

localize14.0ms (0.2%)

rewrite53.0ms (0.8%)

series448.0ms (7%)

simplify66.0ms (1%)

prune164.0ms (2.6%)

localize14.0ms (0.2%)

rewrite48.0ms (0.8%)

series358.0ms (5.6%)

simplify95.0ms (1.5%)

prune117.0ms (1.8%)

localize28.0ms (0.4%)

rewrite72.0ms (1.1%)

series505.0ms (7.9%)

simplify95.0ms (1.5%)

prune315.0ms (4.9%)

regimes469.0ms (7.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (34%)

Profiling