Details

Time bar (total: 3.7m)

sample959.0ms

Algorithm
intervals
Results
597.0ms73×body10240exit
160.0ms84×body2560valid
129.0ms112×body1280valid
21.0ms25×body640valid
16.0ms329×pre80true
7.0ms13×body320valid
3.0ms9×body160valid
2.0ms13×body80valid

simplify231.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
230.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.6b

localize45.0ms

Local error

Found 4 expressions with local error:

29.4b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
16.6b
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
0.1b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(expm1 (* (+ a b) eps))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
26×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
20×add-cbrt-cube add-exp-log
8×associate-/l*
7×cbrt-undiv div-exp
6×pow1 associate-/r* div-inv
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-*r* associate-*l* prod-exp cbrt-unprod
2×clear-num frac-2neg
1×expm1-log1p pow-prod-down *-commutative expm1-udef unswap-sqr associate-/l/
Counts
4 → 108
Calls
4 calls:
Slowest
11.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
10.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
6.0ms
(* (expm1 (* (+ a b) eps)) eps)
0.0ms
(expm1 (* (+ a b) eps))

series929.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
622.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
145.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
113.0ms
(* (expm1 (* (+ a b) eps)) eps)
48.0ms
(expm1 (* (+ a b) eps))

simplify9.5s

Counts
94 → 120
Calls
94 calls:
Slowest
629.0ms
(/ (/ (* (* (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* (+ a b) eps)) eps)) (* (expm1 (* (+ a b) eps)) eps)) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))))
579.0ms
(/ (/ (* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))) (* (* eps eps) eps)) (* (* (expm1 (* eps a)) (expm1 (* eps a))) (expm1 (* eps a)))) (* (* (expm1 (* eps b)) (expm1 (* eps b))) (expm1 (* eps b))))
400.0ms
(* (* (* (expm1 (* (+ a b) eps)) (expm1 (* (+ a b) eps))) (expm1 (* (+ a b) eps))) (* (* eps eps) eps))
398.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
356.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite15.0ms

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×expm1-log1p-u pow1 +-commutative sum-log flip3-+ add-cbrt-cube frac-add add-exp-log flip-+ insert-posit16 log1p-expm1-u
Counts
1 → 35
Calls
1 calls:
Slowest
14.0ms
(+ (/ 1 a) (/ 1 b))

series20.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
20.0ms
(+ (/ 1 a) (/ 1 b))

simplify394.0ms

Counts
27 → 38
Calls
27 calls:
Slowest
52.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))
24.0ms
(* (exp (/ 1 a)) (exp (/ 1 b)))
21.0ms
(/ (sqrt 1) (* (cbrt a) (cbrt a)))
21.0ms
(+ (/ (cbrt 1) a) (/ (cbrt 1) b))
20.0ms
(+ (/ 1 a) (/ 1 b))

prune318.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

16.6b
(/ (expm1 (* eps a)) eps)
16.6b
(/ (/ (expm1 (* (+ a b) eps)) (/ (expm1 (* eps a)) eps)) (expm1 (* eps b)))
5.8b
(/ (expm1 (* (+ a b) eps)) (/ (expm1 (* eps a)) eps))
0.0b
(expm1 (* (+ a b) eps))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
239×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
50×associate-/l*
23×div-inv
20×add-cbrt-cube add-exp-log
19×associate-/r*
10×cbrt-undiv div-exp
5×associate-/r/ log1p-expm1-u
4×expm1-log1p-u pow1 div-sub insert-posit16 expm1-udef add-log-exp
3×clear-num frac-2neg
1×expm1-log1p associate-/l/
Counts
4 → 317
Calls
4 calls:
Slowest
11.0ms
(/ (/ (expm1 (* (+ a b) eps)) (/ (expm1 (* eps a)) eps)) (expm1 (* eps b)))
7.0ms
(/ (expm1 (* (+ a b) eps)) (/ (expm1 (* eps a)) eps))
4.0ms
(/ (expm1 (* eps a)) eps)
1.0ms
(expm1 (* (+ a b) eps))

series879.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
626.0ms
(/ (/ (expm1 (* (+ a b) eps)) (/ (expm1 (* eps a)) eps)) (expm1 (* eps b)))
144.0ms
(/ (expm1 (* (+ a b) eps)) (/ (expm1 (* eps a)) eps))
59.0ms
(/ (expm1 (* eps a)) eps)
50.0ms
(expm1 (* (+ a b) eps))

simplify50.1s

Counts
454 → 329
Calls
454 calls:
Slowest
783.0ms
(/ (/ 1 (/ (* (cbrt (expm1 (* eps a))) (cbrt (expm1 (* eps a)))) (* (cbrt eps) (cbrt eps)))) (sqrt (expm1 (* eps b))))
648.0ms
(/ (/ (* (cbrt (expm1 (* (+ a b) eps))) (cbrt (expm1 (* (+ a b) eps)))) (/ (* (cbrt (expm1 (* eps a))) (cbrt (expm1 (* eps a)))) (* (cbrt eps) (cbrt eps)))) (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))))
529.0ms
(* -1 (/ (- 1 (exp (* a eps))) eps))
527.0ms
(/ (/ (* (cbrt (expm1 (* (+ a b) eps))) (cbrt (expm1 (* (+ a b) eps)))) (/ (* (cbrt (expm1 (* eps a))) (cbrt (expm1 (* eps a)))) (sqrt eps))) (sqrt (expm1 (* eps b))))
477.0ms
(/ (/ (sqrt (expm1 (* (+ a b) eps))) (/ (* (cbrt (expm1 (* eps a))) (cbrt (expm1 (* eps a)))) (* (cbrt eps) (cbrt eps)))) 1)

prune4.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize109.0ms

Local error

Found 4 expressions with local error:

17.1b
(cbrt (expm1 (* eps a)))
17.1b
(cbrt (expm1 (* eps a)))
17.1b
(cbrt (expm1 (* eps a)))
16.5b
(/ (expm1 (* eps b)) (/ (cbrt (expm1 (* (+ a b) eps))) (/ (cbrt (expm1 (* eps a))) eps)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
1371×times-frac
637×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
489×cbrt-prod
137×associate-/r*
29×div-inv
13×add-exp-log
10×add-cbrt-cube
6×cbrt-undiv div-exp
5×associate-/r/
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-/l*
1×clear-num frac-2neg div-sub expm1-udef
Counts
4 → 614
Calls
4 calls:
Slowest
9.0ms
(/ (expm1 (* eps b)) (/ (cbrt (expm1 (* (+ a b) eps))) (/ (cbrt (expm1 (* eps a))) eps)))
1.0ms
(cbrt (expm1 (* eps a)))
1.0ms
(cbrt (expm1 (* eps a)))
1.0ms
(cbrt (expm1 (* eps a)))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
861.0ms
(/ (expm1 (* eps b)) (/ (cbrt (expm1 (* (+ a b) eps))) (/ (cbrt (expm1 (* eps a))) eps)))
128.0ms
(cbrt (expm1 (* eps a)))
124.0ms
(cbrt (expm1 (* eps a)))
120.0ms
(cbrt (expm1 (* eps a)))

simplify2.2m

Counts
989 → 626
Calls
989 calls:
Slowest
895.0ms
(/ (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))) (/ 1 (/ (* (cbrt (cbrt (expm1 (* eps a)))) (cbrt (cbrt (expm1 (* eps a))))) (sqrt eps))))
793.0ms
(/ (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))) (/ (cbrt (sqrt (expm1 (* (+ a b) eps)))) (/ (cbrt (* (cbrt (expm1 (* eps a))) (cbrt (expm1 (* eps a))))) (* (cbrt eps) (cbrt eps)))))
575.0ms
(/ (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))) (/ (* (cbrt (cbrt (expm1 (* (+ a b) eps)))) (cbrt (cbrt (expm1 (* (+ a b) eps))))) (/ (sqrt (cbrt (expm1 (* eps a)))) 1)))
565.0ms
(/ (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))) (/ (cbrt 1) (/ (sqrt (cbrt (expm1 (* eps a)))) (* (cbrt eps) (cbrt eps)))))
554.0ms
(/ (* (cbrt (expm1 (* eps b))) (cbrt (expm1 (* eps b)))) (/ 1 (/ (cbrt (* (cbrt (expm1 (* eps a))) (cbrt (expm1 (* eps a))))) (* (cbrt eps) (cbrt eps)))))

prune8.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes94.0ms

Accuracy

0% (3.3b remaining)

Error of 3.4b against oracle of 0.0b and baseline of 3.4b

bsearch1.0ms

end0.0ms

sample13.8s

Algorithm
intervals
Results
4.7s2550×body2560valid
4.0s3502×body1280valid
3.0s1991×body10240exit
1.1s1016×body640valid
427.0ms9995×pre80true
166.0ms356×body320valid
57.0ms457×body80valid
32.0ms123×body160valid