Details

Time bar (total: 40.4s)

sample512.0ms

Algorithm
intervals
Results
170.0ms112×body1280valid
152.0ms81×body2560valid
122.0ms67×body10240exit
28.0ms36×body640valid
15.0ms323×pre80true
3.0ms7×body320valid
3.0ms16×body80valid
2.0ms4×body160valid

simplify284.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
284.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (- (exp (* b eps)) 1)))

prune35.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 34.8b

localize45.0ms

Local error

Found 4 expressions with local error:

31.8b
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
13.8b
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
0.1b
(* (expm1 (* (+ a b) eps)) eps)
0.0b
(expm1 (* (+ a b) eps))

rewrite36.0ms

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
13.0ms
(* (expm1 (* (+ a b) eps)) eps)
11.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
9.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
1.0ms
(expm1 (* (+ a b) eps))

series952.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
599.0ms
(/ (/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a))) (expm1 (* eps b)))
151.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (expm1 (* eps a)))
137.0ms
(* (expm1 (* (+ a b) eps)) eps)
64.0ms
(expm1 (* (+ a b) eps))

simplify9.6s

Counts
94 → 120
Calls
94 calls:
Slowest
612.0ms
(/ (/ (* (* (* (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))))
583.0ms
(/ (/ (* (* (* (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))))
388.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (+ (* (exp (* a eps)) (exp (* eps b))) 1) (+ (exp (* eps b)) (exp (* a eps)))))
378.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))
344.0ms
(/ (* (- (exp (* (+ a b) eps)) 1) eps) (- (exp (* a eps)) 1))

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

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
11.0ms
(+ (/ 1 a) (/ 1 b))

series12.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
12.0ms
(+ (/ 1 a) (/ 1 b))

simplify354.0ms

Counts
27 → 38
Calls
27 calls:
Slowest
42.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt a) (cbrt a)))
24.0ms
(* (exp (/ 1 a)) (exp (/ 1 b)))
19.0ms
(+ (/ 1 a) (/ 1 b))
18.0ms
(+ (/ 1 a) (/ 1 b))
17.0ms
(/ 1 (* (cbrt a) (cbrt a)))

prune262.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 1 expressions with local error:

14.3b
(/ (+ b a) (* a b))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
6×add-cbrt-cube add-exp-log
4×times-frac associate-/l*
3×add-sqr-sqrt add-cube-cbrt
2×cbrt-undiv div-exp distribute-lft-out associate-/l/
1×expm1-log1p-u pow1 clear-num associate-/r* frac-2neg flip3-+ prod-exp cbrt-unprod flip-+ insert-posit16 log1p-expm1-u div-inv add-log-exp
Counts
1 → 28
Calls
1 calls:
Slowest
22.0ms
(/ (+ b a) (* a b))

series51.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
50.0ms
(/ (+ b a) (* a b))

simplify775.0ms

Counts
19 → 31
Calls
19 calls:
Slowest
241.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a b) (* a b)) (* a b)))
237.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* (* a a) a) (* (* b b) b)))
48.0ms
(+ (pow b 3) (pow a 3))
43.0ms
(- (log (+ b a)) (+ (log a) (log b)))
42.0ms
(- (log (+ b a)) (log (* a b)))

prune245.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

5.6b
(* (/ 1 a) (/ (+ b a) b))
0.0b
(/ (+ b a) b)

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
42×*-un-lft-identity
40×times-frac
26×add-exp-log add-cube-cbrt
16×add-cbrt-cube associate-*r*
13×associate-*l*
9×div-exp
8×prod-exp
7×distribute-lft-out
6×unswap-sqr
5×cbrt-undiv
4×pow1 cbrt-unprod associate-/l*
3×associate-/r* div-inv
2×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp associate-/l/
1×frac-times clear-num frac-2neg flip3-+ pow-prod-down associate-*l/ associate-*r/ *-commutative flip-+
Counts
2 → 98
Calls
2 calls:
Slowest
47.0ms
(* (/ 1 a) (/ (+ b a) b))
29.0ms
(/ (+ b a) b)

series79.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
47.0ms
(* (/ 1 a) (/ (+ b a) b))
31.0ms
(/ (+ b a) b)

simplify4.4s

Counts
93 → 104
Calls
93 calls:
Slowest
444.0ms
(/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* b b) b))
347.0ms
(* (/ (* (* 1 1) 1) (* (* a a) a)) (/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* b b) b)))
321.0ms
(* (* (* (/ 1 a) (/ 1 a)) (/ 1 a)) (/ (* (* (+ b a) (+ b a)) (+ b a)) (* (* b b) b)))
206.0ms
(+ (- 0 (log a)) (- (log (+ b a)) (log b)))
199.0ms
(+ (- (log 1) (log a)) (log (/ (+ b a) b)))

prune848.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes132.0ms

Accuracy

-8% (3.6b remaining)

Error of 3.6b against oracle of 0.0b and baseline of 3.4b

bsearch397.0ms

end0.0ms

sample19.7s

Algorithm
intervals
Results
6.3s2609×body2560valid
5.1s3405×body1280valid
5.1s2011×body10240exit
1.5s10013×pre80true
969.0ms1042×body640valid
253.0ms366×body320valid
108.0ms455×body80valid
46.0ms125×body160valid