Details

sample42.0ms

Algorithm

intervals

Results

7.0ms	189×	body	80	valid
7.0ms	37×	body	1280	valid
6.0ms	27×	body	2560	valid
3.0ms	98×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite109.0ms

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:

64.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(- (* b b) (* (* 4.0 a) c))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
69.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
39.0ms	(- (* b b) (* (* 4.0 a) c))
62.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5001	735

prune282.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
2.4b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.2b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
20.8b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite164.0ms

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:

9.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
57.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* b b) (* (* 4.0 a) c))
131.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
161.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
60.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify120.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	674	2663
1	3462	2412
2	5001	2406

prune443.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize20.0ms

Local error

Found 4 expressions with local error:

7.1b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
8.0b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))))))
21.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite62.0ms

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:

14.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
32.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))))))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series800.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
550.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c)))))))
86.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
85.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	700	2441
1	3372	2185
2	5001	2183

prune486.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.5b

localize21.0ms

Local error

Found 4 expressions with local error:

7.1b	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
7.9b	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))))
21.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))
21.7b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt`
15×	`associate-r`
13×	`add-exp-log`
11×	`times-frac`
10×	`fma-neg` `prod-diff`
9×	`add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `cbrt-prod` `distribute-lft-neg-in` `distribute-rgt-neg-in`
4×	`expm1-log1p-u` `cbrt-div` `flip3--` `prod-exp` `flip--` `log1p-expm1-u`
3×	`associate-l` `unswap-sqr`
2×	`frac-times` `neg-mul-1` `flip3-+` `pow1/3` `diff-log` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 110

Calls

4 calls:

14.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
47.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series796.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
543.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))))
85.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
87.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify168.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	809	2545
1	4462	2237
2	5001	2237

prune506.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.5b

regimes230.0ms

Accuracy

86.1% (3.7b remaining)

Error of 9.3b against oracle of 5.6b and baseline of 32.0b

bsearch174.0ms

Steps

Iters	Range		Point
9	1.074100872074174e-14	9.291103138484119e-07	9.167997088350656e-07
7	2.2469575477562033e-86	4.474843512735295e-85	2.2742398392973687e-86
9	-3.3947692407777386e+132	-4.222463702829868e+123	-8.50694614622187e+125

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	29
1	52	29
2	52	29

end0.0ms

sample1.2s

Algorithm

intervals

Results

248.0ms	1096×	body	2560	valid
220.0ms	5864×	body	80	valid
164.0ms	913×	body	1280	valid
105.0ms	3005×	body	80	nan
70.0ms	459×	body	640	valid
28.0ms	101×	body	5120	valid
22.0ms	212×	body	320	valid
9.0ms	125×	body	160	valid