Details

sample43.0ms

Algorithm

intervals

Results

9.0ms	193×	body	80	valid
9.0ms	42×	body	2560	valid
3.0ms	99×	body	80	nan
3.0ms	16×	body	1280	valid
2.0ms	17×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	5×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 32.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

70.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(- (* b b) (* (* 3.0 a) c))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
49.0ms	(- (* b b) (* (* 3.0 a) c))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune294.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 3.0 a) c))
4.4b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.4b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
20.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 158

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
86.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
59.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b b) (* (* 3.0 a) c))
152.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
191.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify118.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	669	2663
1	3431	2412
2	5001	2406

prune431.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.0b

localize23.0ms

Local error

Found 4 expressions with local error:

7.8b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
8.9b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
20.9b	(cbrt (- (* b b) (* (* 3.0 a) c)))
20.9b	(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`fma-neg` `prod-diff`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `cbrt-prod` `distribute-lft-neg-in` `distribute-rgt-neg-in` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `cbrt-div` `flip3--` `flip--` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
2×	`neg-mul-1` `pow1/3` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `neg-log` `clear-num` `flip-+` `div-inv`

Counts

4 → 99

Calls

4 calls:

17.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
33.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
6.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

series950.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))
640.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
113.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
102.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	699	2442
1	3383	2186
2	5001	2185

prune511.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.0b

localize19.0ms

Local error

Found 4 expressions with local error:

7.8b	(fma -1 b (- (* (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))) (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))))))
9.1b	(/ (fma -1 b (- (* (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))) (fabs (cbrt (- (* b b) (* (* 3.0 a) c))))))) (* a c))
20.9b	(cbrt (- (* b b) (* (* 3.0 a) c)))
20.9b	(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
4×	`pow1` `expm1-log1p-u` `cbrt-div` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `pow1/3` `div-exp` `flip--`
1×	`frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 63

Calls

4 calls:

0.0ms	(fma -1 b (- (* (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))) (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))))))
11.0ms	(/ (fma -1 b (- (* (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))) (fabs (cbrt (- (* b b) (* (* 3.0 a) c))))))) (* a c))
6.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(fma -1 b (- (* (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))) (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))))))
175.0ms	(/ (fma -1 b (- (* (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))) (fabs (cbrt (- (* b b) (* (* 3.0 a) c))))))) (* a c))
100.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))
101.0ms	(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	398	1194
1	1378	1036
2	5001	1019

prune319.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.0b

regimes353.0ms

Accuracy

89.9% (2.7b remaining)

Error of 8.0b against oracle of 5.3b and baseline of 31.7b

bsearch159.0ms

Steps

Iters	Range		Point
8	8.900017451179621e+70	5.1703700736353e+73	1.1187023704581017e+72
8	7.462582960810816e-306	8.206109717114678e-302	7.350002554571356e-304
9	-7.026368034911783e+136	-2.129183190182848e+131	-5.5713700198328724e+135

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	38
1	64	38
2	64	38

end0.0ms

sample1.1s

Algorithm

intervals

Results

217.0ms	5908×	body	80	valid
215.0ms	1025×	body	2560	valid
138.0ms	844×	body	1280	valid
98.0ms	2941×	body	80	nan
58.0ms	456×	body	640	valid
30.0ms	119×	body	5120	valid
24.0ms	228×	body	320	valid
7.0ms	101×	body	160	valid