Details

sample48.0ms

Algorithm

intervals

Results

12.0ms	194×	body	80	valid
7.0ms	30×	body	2560	valid
6.0ms	100×	body	80	nan
6.0ms	28×	body	1280	valid
2.0ms	14×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
1.0ms	6×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* 3.0 a) c)
1.2b	(- (* b b) (* (* 3.0 a) c))
1.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
45.0ms	(- (* b b) (* (* 3.0 a) c))
72.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	337	530
1	1440	479
2	5002	467

prune253.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
1.2b	(- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))
1.9b	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
23.0b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `distribute-rgt-neg-in` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `distribute-lft-neg-in` `sqrt-prod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `pow1/3` `diff-log` `prod-diff` `neg-log` `flip-+`

Counts

4 → 73

Calls

4 calls:

0.0ms	(cbrt c)
3.0ms	(- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))
14.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
4.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series411.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt c)
59.0ms	(- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))
93.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
87.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	308	850
1	1236	747
2	5001	690

prune280.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
1.2b	(- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))
1.9b	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))))
23.0b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `distribute-rgt-neg-in` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `distribute-lft-neg-in` `sqrt-prod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `pow1/3` `diff-log` `prod-diff` `neg-log` `flip-+`

Counts

4 → 73

Calls

4 calls:

0.0ms	(cbrt c)
3.0ms	(- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))))
4.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt c)
61.0ms	(- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))
101.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))))
88.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))

simplify53.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	320	1340
1	1350	1203
2	5002	1083

prune314.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.3b

localize29.0ms

Local error

Found 4 expressions with local error:

1.9b	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))))
23.0b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))
23.0b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))
23.0b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `distribute-rgt-neg-in` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `flip-+`

Counts

4 → 78

Calls

4 calls:

11.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))))
4.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))
4.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))
4.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))

series354.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c)))))))
86.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))
86.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))
87.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (* (* (cbrt (cbrt c)) (cbrt (cbrt c))) (cbrt (cbrt c))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	249	1688
1	1038	1614
2	5002	1599

prune431.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.3b

regimes298.0ms

Accuracy

84.8% (3.4b remaining)

Error of 15.5b against oracle of 12.1b and baseline of 34.4b

bsearch139.0ms

Steps

Iters	Range		Point
10	7.948130497386624e-31	1.6081733637561173e-14	5.082297393178073e-29
9	-2.2154171522802282e+61	-2.0511250318755918e+53	-2.0697892322852844e+57

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	27
1	37	27

end0.0ms

sample1.4s

Algorithm

intervals

Results

394.0ms	5935×	body	80	valid
260.0ms	1018×	body	2560	valid
188.0ms	2907×	body	80	nan
186.0ms	882×	body	1280	valid
74.0ms	435×	body	640	valid
37.0ms	116×	body	5120	valid
34.0ms	252×	body	320	valid
10.0ms	106×	body	160	valid