Details

Time bar (total: 5.4s)

sample54.0ms

Algorithm
intervals
Results
13.0ms188×body80valid
9.0ms33×body2560valid
7.0ms97×body80nan
6.0ms26×body1280valid
3.0ms15×body640valid
2.0ms12×body320valid
0.0ms1×body5120valid
0.0ms3×body160valid

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×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 → 157
Calls
4 calls:
45.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
18.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series282.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms
(- (* b b) (* 4.0 (* a c)))
75.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
66.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify76.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05903305
121012212
250022169

prune360.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
1.2b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
60×add-sqr-sqrt
57×*-un-lft-identity
49×add-cube-cbrt
35×sqrt-prod
23×add-exp-log distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×prod-exp add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-*l*
5×flip3-- flip--
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp 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 → 165
Calls
4 calls:
61.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
3.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series285.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
44.0ms
(- (* b b) (* 4.0 (* a c)))
77.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify90.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
06563423
125942238
250012193

prune329.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×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 → 157
Calls
4 calls:
45.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series296.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
51.0ms
(- (* b b) (* 4.0 (* a c)))
81.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify75.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05903305
121012212
250022128

prune310.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ 1 (* 2.0 a)))
1.2b
(- (* b b) (* 4.0 (* a c)))
1.4b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
7×cbrt-prod neg-mul-1
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×flip3-- times-frac diff-log flip--
2×sub-neg sqrt-div distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square cbrt-div sqrt-pow1 pow1/2 pow1/3 neg-log div-inv
Counts
4 → 141
Calls
4 calls:
3.0ms
(cbrt (/ 1 (* 2.0 a)))
4.0ms
(- (* b b) (* 4.0 (* a c)))
17.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series392.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(cbrt (/ 1 (* 2.0 a)))
48.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify74.0ms

Algorithm
egg-herbie
Counts
153 → 153
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04592954
114641916
250021821

prune322.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.6b

regimes258.0ms

Accuracy

84.7% (4.4b remaining)

Error of 10.3b against oracle of 5.9b and baseline of 34.8b

bsearch160.0ms

Steps
ItersRangePoint
11
3.0336165705843857e+124
3.3022304128508224e+146
9.181091926046939e+128
10
-2.4076762225838956e-89
-7.528955394503449e-103
-2.37327700068816e-89

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03716
13916
23916

end0.0ms

sample1.6s

Algorithm
intervals
Results
424.0ms5758×body80valid
302.0ms1056×body2560valid
234.0ms967×body1280valid
209.0ms2885×body80nan
92.0ms461×body640valid
42.0ms223×body320valid
35.0ms103×body5120valid
15.0ms116×body160valid