Details

Time bar (total: 4.8s)

sample42.0ms

Algorithm
intervals
Results
8.0ms35×body2560valid
8.0ms194×body80valid
5.0ms27×body1280valid
3.0ms84×body80nan
2.0ms14×body640valid
1.0ms9×body320valid
1.0ms3×body5120valid
0.0ms3×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite54.0ms

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:
34.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series501.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
244.0ms
(- (* b b) (* 4.0 (* a c)))
83.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0404890
11481801
25001796

prune250.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.6b
(- (* b b) (* 4.0 (* a c)))
0.9b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite79.0ms

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

series298.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
49.0ms
(- (* b b) (* 4.0 (* a c)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
73.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0469991
12048866
25002857

prune241.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
3.2b
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
8.2b
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
76×add-sqr-sqrt
63×*-un-lft-identity
52×times-frac
51×add-exp-log
30×add-cube-cbrt associate-*l*
27×add-cbrt-cube
20×prod-exp difference-of-squares
16×div-exp
13×sqrt-prod distribute-lft-out
10×distribute-lft-out--
8×cbrt-undiv cbrt-unprod
7×pow1 associate-*r*
6×associate-/r* add-log-exp
4×rec-exp flip3-- 1-exp associate-/r/ flip-- associate-/l*
3×div-inv
2×sqrt-div associate-/l/ unswap-sqr
1×frac-times sub-neg rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down associate-*l/ clear-num un-div-inv *-commutative flip-+
Counts
4 → 152
Calls
4 calls:
20.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
66.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
26.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series524.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
167.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
205.0ms
(/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify115.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
07642421
137162067
250012044

prune412.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b b) (* 4.0 (* a c)))
1.2b
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
12.6b
(/ (* 4.0 (* a c)) (* 2.0 a))
22.5b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log add-cbrt-cube
10×add-sqr-sqrt
9×prod-exp cbrt-unprod
8×add-log-exp
7×*-un-lft-identity
6×cbrt-undiv div-exp
5×pow1 add-cube-cbrt
4×sqrt-prod
3×flip3-- flip--
2×sub-neg sqrt-div diff-log difference-of-squares
1×rem-sqrt-square frac-2neg sqrt-pow1 times-frac pow1/2 clear-num associate-/r* div-inv associate-/l* distribute-lft-out--
Counts
4 → 67
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
18.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
8.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series211.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms
(/ (* 4.0 (* a c)) (* 2.0 a))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0403576
12221498
25001498

prune189.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.5b

regimes178.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.4b against oracle of 5.4b and baseline of 29.8b

bsearch148.0ms

Steps
ItersRangePoint
6
1.1594993669073426e+93
1.3006782908792091e+94
3.547431856925436e+93
9
1.0330294288086087e-261
2.084324433095697e-255
1.567927026193799e-258
6
-1.1860998636736231e+119
-2.8360830985906895e+118
-1.1730875761889226e+119

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04524
14724
24724

end0.0ms

sample1.2s

Algorithm
intervals
Results
252.0ms1034×body2560valid
239.0ms5816×body80valid
180.0ms910×body1280valid
116.0ms2947×body80nan
72.0ms451×body640valid
37.0ms126×body5120valid
25.0ms219×body320valid
10.0ms126×body160valid