Details

Time bar (total: 11.8s)

sample242.0ms

Algorithm
intervals
Results
87.0ms82×body2560valid
64.0ms64×body10240exit
53.0ms108×body1280valid
12.0ms43×body640valid
6.0ms320×pre80true
2.0ms12×body320valid
1.0ms11×body80valid

simplify100.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04013
110113
225813
376613
4389513
5500113

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
1.3b
(- (exp (* a eps)) 1.0)
3.0b
(- (exp (* b eps)) 1.0)
4.3b
(- (exp (* (+ a b) eps)) 1.0)

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
49×*-un-lft-identity
45×prod-diff
39×add-cube-cbrt
11×distribute-rgt-in distribute-lft-in
10×add-log-exp
9×flip3-- fma-neg flip--
6×pow1 add-exp-log add-cbrt-cube
5×sub-neg associate-*r* associate-*l* distribute-lft-out-- difference-of-squares
4×expm1-log1p-u frac-times log1p-expm1-u
3×diff-log
2×associate-*r/ associate-*l/
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 138
Calls
4 calls:
11.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
5.0ms
(- (exp (* a eps)) 1.0)
5.0ms
(- (exp (* b eps)) 1.0)
5.0ms
(- (exp (* (+ a b) eps)) 1.0)

series165.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
38.0ms
(- (exp (* a eps)) 1.0)
31.0ms
(- (exp (* b eps)) 1.0)
47.0ms
(- (exp (* (+ a b) eps)) 1.0)

simplify63.0ms

Algorithm
egg-herbie
Counts
150 → 150
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04881660
120511241
250031216

prune481.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 48.3b

localize30.0ms

Local error

Found 4 expressions with local error:

3.4b
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
4.3b
(- (exp (* (+ a b) eps)) 1.0)
13.3b
(* (pow eps 2) (pow b 2))
17.5b
(* (pow eps 3) (pow b 3))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
63×add-sqr-sqrt
40×add-exp-log
32×unswap-sqr
28×unpow-prod-down
23×*-un-lft-identity
22×prod-exp
21×add-cube-cbrt
20×associate-*r* associate-*l* add-cbrt-cube sqr-pow
14×cube-prod
12×pow-to-exp pow-exp
10×unpow2
9×prod-diff
6×cbrt-unprod add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×flip3-- fma-neg flip--
2×cube-mult unpow3 associate-*r/ pow-prod-down associate-*l/ associate-/r/ *-commutative associate-/l/
1×sub-neg frac-2neg times-frac diff-log clear-num associate-/r* div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 169
Calls
4 calls:
14.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
8.0ms
(- (exp (* (+ a b) eps)) 1.0)
8.0ms
(* (pow eps 2) (pow b 2))
9.0ms
(* (pow eps 3) (pow b 3))

series1.7s

Counts
4 → 12
Calls
4 calls:
1.5s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
46.0ms
(- (exp (* (+ a b) eps)) 1.0)
32.0ms
(* (pow eps 2) (pow b 2))
67.0ms
(* (pow eps 3) (pow b 3))

simplify136.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 2 (119.0ms)

IterNodesCost
07851816
146731415
250011412

prune717.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (/ 1 b) (/ 1 a))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
15×times-frac
13×fma-def
10×add-sqr-sqrt add-cube-cbrt
7×distribute-lft-out
5×div-inv
3×add-log-exp
1×pow1 add-exp-log +-commutative expm1-log1p-u flip3-+ frac-add sum-log add-cbrt-cube flip-+ log1p-expm1-u
Counts
1 → 34
Calls
1 calls:
13.0ms
(+ (/ 1 b) (/ 1 a))

series13.0ms

Counts
1 → 3
Calls
1 calls:
13.0ms
(+ (/ 1 b) (/ 1 a))

simplify68.0ms

Algorithm
egg-herbie
Counts
37 → 37
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
0107112
1368101
2127498
3314498
4500198

prune77.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
0.6b
(cbrt (+ (/ 1 b) (/ 1 a)))
0.6b
(cbrt (+ (/ 1 b) (/ 1 a)))
0.6b
(cbrt (+ (/ 1 b) (/ 1 a)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
139×*-un-lft-identity
114×cbrt-prod
81×distribute-lft-out
60×div-inv
42×times-frac
37×add-sqr-sqrt
33×cbrt-div swap-sqr
29×add-cube-cbrt
13×associate-*r* associate-*l*
11×pow1 flip3-+ frac-add flip-+
9×frac-times pow1/3
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
3×associate-*r/ associate-*l/
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 167
Calls
4 calls:
31.0ms
(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
12.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))
12.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))
15.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))

series342.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
81.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))
81.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))
80.0ms
(cbrt (+ (/ 1 b) (/ 1 a)))

simplify67.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04021859
116191609
250021449

prune322.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes61.0ms

Accuracy

0% (3.0b remaining)

Error of 3.5b against oracle of 0.5b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
093
193

end0.0ms

sample7.0s

Algorithm
intervals
Results
2.6s2605×body2560valid
1.8s1989×body10240exit
1.7s3438×body1280valid
293.0ms1019×body640valid
169.0ms9989×pre80true
65.0ms346×body320valid
26.0ms466×body80valid
16.0ms126×body160valid