Details

sample65.0ms

Algorithm

intervals

Results

15.0ms	39×	body	2560	valid
14.0ms	189×	body	80	valid
13.0ms	31×	body	1280	valid
5.0ms	72×	body	80	nan
3.0ms	11×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

37.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune237.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt` `times-frac` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

33.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series471.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
73.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
47.0ms	(- (* b b) (* 4.0 (* a c)))
261.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune223.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.0b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b	(- (* b b) (* 4.0 (* a c)))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`div-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
3×	`times-frac` `diff-log`
2×	`cbrt-undiv` `frac-times` `sub-neg` `rec-exp` `distribute-rgt-neg-in` `sqrt-div` `1-exp` `associate-*l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

55.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
12.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
42.0ms	(- (* b b) (* 4.0 (* a c)))
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	469	991
1	2048	866
2	5002	857

prune222.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.6b

localize16.0ms

Local error

Found 4 expressions with local error:

23.0b	(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
23.8b	(cbrt (- (* b b) (* 4.0 (* a c))))
23.8b	(cbrt (- (* b b) (* 4.0 (* a c))))
23.8b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
30×	`flip3--` `flip--`
28×	`frac-times`
26×	`sqrt-div`
24×	`pow1`
15×	`sqrt-pow1`
14×	`associate-*l/`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
8×	`associate-*r/`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 89

Calls

4 calls:

33.0ms	(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
2.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
2.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
2.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series353.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (* (* (cbrt (- (* b b) (* 4.0 (* a c)))) (cbrt (- (* b b) (* 4.0 (* a c))))) (cbrt (- (* b b) (* 4.0 (* a c))))))
95.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
94.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
94.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify188.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 3 (168.0ms)

Iter	Nodes	Cost
0	347	1856
1	914	1805
2	4113	1785
3	5001	1704

prune293.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 6.6b

regimes225.0ms

Accuracy

83% (4.9b remaining)

Error of 10.5b against oracle of 5.6b and baseline of 34.5b

bsearch111.0ms

Steps

Iters	Range		Point
8	6.881289457293598e+137	5.567978725714423e+140	6.852645386257879e+139
6	-1.2951389239126576e-136	-2.560718984586591e-137	-1.279587145681289e-136

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	17
1	43	17
2	43	17

end0.0ms

sample1.8s

Algorithm

intervals

Results

449.0ms	5796×	body	80	valid
417.0ms	1111×	body	2560	valid
286.0ms	914×	body	1280	valid
202.0ms	2910×	body	80	nan
109.0ms	452×	body	640	valid
48.0ms	101×	body	5120	valid
43.0ms	231×	body	320	valid
15.0ms	113×	body	160	valid